310-065 exam Dumps Source : Sun Certified Programmer for the Java 2 Platform.SE 6.0

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310-065 exam Dumps Source : Sun Certified Programmer for the Java 2 Platform.SE 6.0

Test Code : 310-065

Test designation : Sun Certified Programmer for the Java 2 Platform.SE 6.0

Vendor designation : SUN

: 305 true Questions

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Continue without consentCompactificationThe first problem I contemplate with this thought is that the definitions are not well defined. respect 1/0=inf. Then inf=(1/0)*(-1/-1)=(1*-1)/(0*-1)=-1/0=-inf.A similar string of equalities gives 'nullity' being equal to both inf and -inf.

Zav"Imagine you're landing on an aeroplane"Landing ON an aeroplane? which fraction of the aeroplane should I land on?

HiI enjoy how he never really proves anything. sum he says is "0/0=nullity." Okay? What's wrong with motto NAN? "Well," he would say, "Nulity is actually a number." Well that's great, but why cant you add it,subtract it, multiply it, divide it, accomplish exponents, or accomplish roots with it? Why does it mess of everything they already know about math? If the only contrast between this "nullity" and NaN is that "nullity" is cnsidered a number, then I absorb an idea. Why not sigh "aN" for "A Number."

Dangercrowx divided by x is always 1, so why would 0 over 0 be any different, it should be 1

IanFirst of all, if you are so opposed with the definition of a number nullity=0/0, why accomplish most absorb no problem with the definition i^2=-1?? there is no contrast in the fact that they are both definitions of a non-real numberMost of the comments here besides withhold using the 1=2 fallacy. This fallacy uses the assumption that 0/0=1, which is not honest in transreal arithmetic. In transreal arithmetic, you would Get the result nullity*1=nullity*2, which is true.Also, the limiting process is not vital here, because it only looks at values proximate to the number in question, they could define the actual number as nullity without losing the concept of limits.Nullity is different from NaN, for the simple reason that, while NaN does not compare to itself, nullity is equal to itself. Every time.Even if they absorb no employ for it now, who says they will never ascertain one???

DazliaHow accomplish they unravel an unsolvable math problem? fabricate a fresh number and sigh it's the answer!!!

Pharme791Very nice site!

Joe"nullity - which sits outside the conventional number line (stretching from negative infinity, through zero, to positive infinity)"Nothing over Nothing = Everything? This doesn't fabricate any sense to me...

PXwhat he is motto doesn't fabricate sense. it's better to sigh that x/0 is infinity, since any number would felicitous in it. Assuming 0/0 is that nullity thing, does 0 times nullity equal 0? explain that on his number line. How arrive when you graph x/0, and you examine at the 0 point, the line is really at infinity? He obviously thought that he could just accomplish what people did with square rooting negative numbers, which he can't, since the square root of negative one actually does exist, just not in the true number system. dividing something by zero isn't impossible, you just can't accomplish it. Imagine you absorb a trillion apples. You want to divide them evenly between zero people. How many does each person get? theres no people to give the apples too. It's not enjoy every person gets nullity, there's just no one to give anything to.

Rajiv AmlaniTeaching kids a pile of rubbish. Shouldn't be teaching mathematics if you contemplate 'nullity' solves a 1200 year problem. Clown.

ChrisHe claims that 0/0 is nullity, a sole number with a positive (albeit not strictly real) value, yet they know every true and complex number solves 0/0=x, so it is not a sole number, it is undefined, it really is that simple. What he is motto is simply incorrect. besides 1/x as x tends to 0 does minister to infinity, but 1/0 (and indeed a/0 where a is not equal to 0) is not equal to infinity, it is indeterminate, which is to sigh there is no value which solves 1/0=x. Infinity is not a number it is the concept "as large as they want", for 1/0 "as large as they want" is soundless not large enough.

me1=2

shoopofthedayit's basically the concept of imaginary numbers, except those are actually useful sometimes.

very ingenious oneHey! i just establish a way, how can EVERYONE multiply two numbers just in a sec or two! Let's say, that every number which is greater than multiplied by ANY number is equals to BIGGETY. I hope i helped sum the mathematic and broad number problems, maybe solved the spaceship problems as well.

Kenneth WongThis would defeat calculus. On a limit, the undefined is usually really important. To my understanding. Im soundless in middle school.

KazemiI. Hate. Him. That guy is a cheat. He just says 'Oh, hey, this here is a fresh symbol I "made" whose sole purpose is to divide by zero!' A lot of safe that does us.

achthe "we employ 0/0 in calculus" dispute is stupid. people, they accomplish not Get the value of 0/0 in calculus. they Get its limit. there's a difference.

Bernard AzakieBritish schoolchildren "stupid"Have a nullity doesn't change anything. Your system will spit out "nullity" upon crash, but won't actually change anything. Whether something crashes gently or not is just a matter of crash handling.

DavidEXPANDING FAILLLL YUSHIN WASHIO.x*(y/x) = y if x and y are INTERGERS not equal.If you expand using zero, it will clearly give zero.Division by zero is NOT workable using the RNS. nor is finding the SQRT of -1.

Sam O'Nouny"Nullity" is utter bupkis. It's just another pass of motto "Not a Number", "Undefined", "Indeterminate", and of course, "Error". One cannot divide or be divided by zero. After all: 0/0=X; 0=X*0; therefore, X=All true Numbers, causing it to be undefined. Or is it +inf and -inf? *shrugs*PS-Rearrange "Sam O'Nouny" and you Get "Anonymous".

Yushin WashioSimilar to the imaginary unit, it would be more useful to define 1/0 rather than 0/0 becuase anything is 0 if you multiply it with 0. So, 0*1=0, 0*0=0, 256*0=0 and even i*0=0. So, 0*(1/0)=0. However, since always x*(y/x)=y, 0*(2/0) must be =2, 0*(3/0)=3 and 0*(i/0)=i should sum be right. Therefore, if 0^-1 is not simple enough for you, you can define your "nullity" as:0*1*nullity=1but 0*nullity=0and 0*-1*nullity=-1However, since the nullity itself without 0 is not defined, 1*nullity or -1*nullity remain undefined.

raymondlangley@tiscali.co.ukgreat news, now relate me how can i Get my ten year traditional to learn divisions .. he knows his time table in head from 1/15 times but he just cannot understand divisions no matter how difficult i try ...help please...

Siyang ChenThis is neither fresh nor useful. Computers already absorb the equivalent of a 'nullity' (NaN) in every reasonable floating point data type. Moreover, this does not divulge anything about dividing by zero that they did not already know (meaning, that the operation cannot produce any meaningful result with other arithmetic operations). Hooray for relabling an traditional concept and claiming credit for it. Maybe I'll retreat ascertain gravity tomorrow.

DanniThis is bullshit and he SHOULD know better. If he'd asked any one in the mathematics community he'd absorb known he wasn't solving a problem because there was no problem to commence with!He hasn't even checked to contemplate sum the contradiction his theory presents.There are tons of ways to drudgery around the problem, the projective line being a very practical example. AND they those ways are more theoretically sound and non-contradictory. I won't bother to explain it because obviously no one is interested in hearing true mathematicians talk. It's not enjoy they just spent their terminal five years intensely studying it or anything. Never humor us.

MorpheusTake the blue pill, Mr Anderson.

Disagree1*0=2*0divide both by zero (which is an immposability)and you absorb 1=2this number CAN'T be realand even if it was zero is the concept of nothing...infinity would be everything and so cancel it out not "nullity"

PaulThis is ridiculous. Dividing by zero is not a "problem," it's a mathematical impossibility. Inventing a designation for an entity that doesn't exist doesn't antecedent that entity to exist.Look at it this way. You relate me there's no animal made out of cheese. I sigh yes there is, it's called a froopsie. And then I write, like, twelve papers based on the actuality of the froopsie and how I've solved the cheese-animal problem. The froopsie soundless doesn't exist, and I haven't solved the problem.Not only is Dr Anderson displaying a basic lack of understanding concerning why this "problem" can't be solved, but he's passing it on to those poverty-stricken schoolchildren. Maths education is despicable enough already. This man should be stripped of his teaching licence.

YanThis all thought is utterly pointless. This man is just making up a fresh word for NaN, or undifined. And if someone can arrive up with a practical employ for this, I won't belive it.

MarkThis fresh number has profound effects on the computing industry, by allowing the division of zero by zero many errors that absorb previously made things impossible absorb become quite possible.

Aaron J. Lang (phantom.penguin@hotmail.co.uk)I'm currently studying maths at GCSE but am one of if not the top in my year. The equations he does on the birthright are difficult to read in the video but I absorb a problem with the "definitions" he puts up on left, he simply states them, no explanation or deriving or anything. If anybody knows where I can find this then gratify relate be, if not then his theory is just too unsupported to be taken seriously. P.S. I positive the greek note "phi" that hes using for "nullity" is already assigned to (((5^0.5)+1)/2). if its not and im being really blonde gratify contact me (address above), i really would enjoy to understand this.

Tayler WamplerOK well I contemplate this guy is quack. If you *can* divide by zero, then wouldn't everything in Math be a lie? And pretty much, this is so useless. Who's ever gonnahave to divide by zero? People absorb been doing Math how we're doing it now for.....I waver to sigh forever.....but a *very* long time. What's this guy trying to do, anyway? Create a revolution? Not gonna happen.

sarahi thought zero plus zero = zero. i besides thought zero divided by zero was zero???

Scrapdogx * 0 = 4 unravel for x.

GarashI always knew that such a number existed, if you seize out your Ti-83 plus, on the graphic section, you write 1/x, you can contemplate in the graphic that a nomber that would picture 1/0 would be sum the number, wicht is imposible in a fonction...

freddyIts not such a broad deal. I stand for c'mon so there is a fresh number that noone is going to employ anyway. Woop-de-de,How many times are you going to divide something in true life by 0 anyway. It is just one of those pointless questions they stick on an exam.

ConfusedI todally accomplish not Get it. I stand for how in the world can 0/0=infinity? It is just plain cofusing! I guese that it might fabricate more sense when ever I Get taught it, but untill then I guese that I will just absorb to be confused. Ta, Ta for now!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

kalebThis is stupid. It 'solves' nothing. It still, basically, says that X/0=NaN. It's a useless concept. Perhaps it will aid computors, but it changes nothing mathimatically.

that guyi just divided my pacemaker by 0, but i havent died yet

a lofty school physics studentanother thing... phi is already a symbol for flux... nothing new

a lofty school calculus studentcalculus - where they divide, add, subtract, and multiply by zero and infinity retreat Get true answers sum the time...

nikko holti contemplate this guy needs to retreat back to the drawing board. i don't contemplate why they let him train this to kids enjoy you always sigh fabricate complicated things simple he's making things pass more complicated.

ron jonesone divided is technically ifinity

Hmm...Fantastic! Extra stuff to learn at school!

MozeyThis guy basically reclaim some sounds together, drew some lines and got a word and a badge for undefined. yoopdeedoo. The incredible fraction is he confused one of the first things i erudite in elementry math, you cant divide be zero. This just messes up the pass i think. It goes against 'the essence of mathmatics is to fabricate complicated things simple. Not fabricate simple things complicated.' It just doesn't drudgery Mr.Frazier.

Alexis PeneffKind off It would fuddle me at first. But after a while i would Get it. The theory is a bit strange. It will seize even more years to Get the calculators and computers to absorb nullity. I dont contemplate that my math scholarship couldn't be divided by zero. It would seize my brain a lot longer to Get this know then if someone created it when i first started math. My brain is already used to the traditional mode way. Other prudent i contemplate it is a safe theory. Though i absorb never tried to divide by zero.

Sameera. KI am doing a physics coursework in which i am investiagtign whether how the thickness of the wire affects the resistance. However on one of my graphs, which is one over thickness, my teache rhas asked me whether or not the graph has to retreat through the origin. But I establish out that one over zero equals infinity, thereofore how can that be represented on a graph? However if thinking logically is there is zero thickness then there will absorb to be zero resistance. This is why I ma quite confused.

Azathoth0/0 = X 0 = X * 0 So zero times what equals zero. Thats birthright boys and girls. Every sole number that exists. ... This is why it comes up undefined. DUH... If they want to arrive up with a symbol that represents any number, retreat for it. But its kinda pointless. 0/0 = anynumber, it equals 1, and 2, and 50 and 100 and 5000, and 2^58, and 281! and sqrt(1.52x10^235409) and 0 and i and -i... etc etc... accomplish you Get it yet? No DEFINATE answer. the reply is a variable that covers sum possibilities.

LOLWhat the hell? Making up another number is not solving things -_-

aloofphila distinguished number of the below comments point out the various flaws in dr. anderson's idea. the value in it (if any) is that in mathematics you can define any element you want, as long as you are consistent with the accepted axioms and conventions. from a mathematical standpoint dr. anderson is just being silly, from an educational standpoint he's teaching his students a bit about how the mathematics progresses and how it has become the field it is today. unfortunately, he’s not consistent with that which has arrive before him.

adammany people are forgetting, or simply haven't worked with higher math, but in calculus classes they very often drudgery with problems that would antecedent division by zero. In many of the problems its as simple as changing some of the variable to more integratable or differentiable variables and derivating or integrating... seize a calculus class before relating surmise that you know, obviously, very shrimp about. Oh, and P.S. the solutions to many of these problems varies with each circumstance and the equations chosen, so, e.q. 0/0 could equal 1 or infinity or a set number.

The Anonymous RhoI contemplate everyone is delving too deep in the operation of division. Division, in its simplest form, is repeated subtraction (by its very definition). So, 20/5 is 4 because they can subtract 5 four times from 20 until they hit zero. So, let us examine 1/2. This equals one-half because they can subtract 2 one-half times and Get zero. Great. Now, 0/1 is zero because they need to subtract 1 zero times from zero to obtain zero. Fabulous. What about 1/0? How many times must they subtract zero from 1 to obtain zero? Oops! That can't happen. That's why 1/0 is undefined. What about 0/0? How many times can they subtract zero from zero to obtain zero? Well, this seems indefinite. Could be 1, 2, or 1x10^2001. So, 0^0 is besides undefined. Dr. Anderson makes conventions for the sake of making conventions; they can define 4/2=infinity. That's a convention. Let's not mention the fact that Dr. Andersen uses the laws of exponents for his lousy dispute or that the laws of exponents only drudgery for true numbers, so his arithmetic does not drudgery with his fresh number 'nullity'.

PoochyOkay, so he basically gave x/0 a fresh name, and completely against the meaning of 0/0 (see l'Hospital's Rule). I fail to contemplate how this is revolutionary, unless re-naming stuff and making it convoluted is revolutionary. If that's revolutionary, I'd enjoy to announce a revolutionary concept of my own: Plard. It's a constant that's between 0.5 and 0.6, approximately 0.573. Now gimme a Nobel Prize for my revolutionary concept. Also, the computer science aspect already has a perfectly safe solution - the try-catch statement.

BenSo essentially he just took the word "undefined" and gave it a symbol that he's calling nullity? I'm positive there's more to it than that, but that's what it looks enjoy to me. Just trying to give computers a pass to understand "undefined."

markI contemplate Dr. Anderson just proved the existance of god....

Peabnuts123I know the exact sort of person this guy is; they sum do. He's that guy who is always trying too difficult to be positive, to listen to everyone's ideas, and to think, to actually BELIEVE they are correct. My deputy principal is just enjoy this guy. I can contemplate this guy sitting in his office, or wherever, talking to his buddies motto "i don't contemplate why everyone thinks this all 'divide by zero' thing is so hard. Why not just create a fresh number to account for it? It's really quite simple". Thinking about the theory itself, enjoy someone mentioned previously, dividing 6 apples by 2 give 2 groups. Thus dividing by 0 gives 0 groups. Also, when multiplying the previously exampled two groups by two, you Get the original six. If you absorb divided something into nothing, then multiplying backwards by any amount, will soundless give nothing. Thus proving anything(besides 0)/0=0.

JoeLook, here's how it is. x^1=x, right? And to Get x^0, you divide x^1 by x. They already know that x^1=x, so they can sigh that x/x=x^0. This is the obvious part. Now, if they fabricate x = 0, then we're motto that 0/0=0^0, or written differently 0^0=0/0. Dr Anderson is motto that 0^0=nullity. He already said that nullity is just 0/0. So basically he just proved that 0/0=0/0. Which is great.

Joe WhiteheadI was positive that was not the only one to contemplate of 'innumeracy' constants! It's icy to contemplate someone finally find a employ for them. The problem is that the division isn't reversible. ;) The fact that one infinity may not be the same as another is another issue sum together.

Math fanTo Kevin: It is not 1 divided zero times. It is 1 divided into 0 groups. When you absorb 1 divided by 2, you are not dividing 1 two times. That would create 3 groups. You are making 2 groups. So the problem arises when you try to fabricate 0 groups. Also, there is the principle that 0 divided by anything is 0. In the case of 0/0, it contradicts the principle that anything divided by itself equals 1.

creepxthis is just ridiculous! there's no consistent pass of defining a division by zero as a number. you will only discontinuance up in inconsistency.

AlyssaNO! you can't divide by zero. it's impossible. i will roar if you can divide by zero. no lie. it will prove that every sole thing in math was a lie. i abominate math.

Okinaptz UglwfSo "nullity" is "outside the conventional nubmer line". In other words, nullity, as x/0, is not defined "inside the conventional number line". broad deal, really ...

Some guyDivision by 0 is not possible. Just examine at the graph of 1/x. As x approaches 0, f(x) approaches +/- infinity. For this reason, anything divided by 0 cannot be 0, as somebody else said. Plus... If x/0 is defined, then you can prove that 1=2.

AdamHaving encountered Dr Anderson at university, I absorb a more specific comment. He could accomplish with marking some students drudgery instead of spending his time naming undefined numbers. Here's my fresh number - it's called 'the answer'. Give me any problem - the solution is my fresh number. In conclusion, Dr Anderson is a computer scientist and not a mathematician - there is a world of difference.

pr0pr0the problem i absorb with this, is its not really math, they are inventing a number to fill in a missing piece of a puzzle, which is *far* from complex math. dividing by zero does not give anyone any ANY useful mathematical numbers OR formulas, it is the same if the result is "nullity", which would really be no different then an error message: it soundless serves no purpose to mathematics as a whole. spending your life calculating pi and trying to find an discontinuance is more useful then "nullity" (mainly because it would withhold Dr James Anderson assiduous so they wouldn't absorb to endure more of this kindergarten math... summary: if you could just invent a number to unravel a thousand year traditional math problem A. its takes away sum legitimacy of said problem B. Roman mathamaticians could absorb easily thought of it: if it was a safe thought (which it isnt)

JohnWhat about this? 0 = 1 / ∞ 0 = 0/1 0/1 = 1/∞ (Cross multiply) 0*∞ = 1*1 The sum of illimitable 0’s soundless amounts to 0 so: 0 = 1. Isn't this the same line of thinking?

PhredFor those interested in understanding the topic of zero, I recommend Charles Seife's book, "Zero: The Biography of a uncertain Idea." Of particular interest is the first appendix, which uses the 0=1 proof to present that Winston Churchill is a carrot.

Aaron2 divided zero times is not two. Dividing it zero times gives you zero parts of a sum. Imagine dividinig 2 a half a time if you can. You Get 4. Dividing two a quarter of a time gives you 8. seize this infinitely proximate to zero and your reply approaches infinity, not 2.

Senor BSThis is utter BS. 0/0 is the exact antithetical of "Nullity". It's defined as some number which, when multiplied by zero, would equal to zero. This means that 0/0 is equal to sum numbers, rather than none. BS.

MaxI contemplate fraction of the problem arises due to the pass zero (0) is used alternately to picture void (nothing) or the infinitely little 1/inf. Void isn't 1/inf, void (0) would be more appropriately linked to "Not a Number" (NAN). The infinitely little soundless has size and illimitable progressions never achieve zero. It's always puzzled me how slack mathematicians are when considering stuff enjoy this. Far from being rare probs enjoy this crop up sum the time in computing and programmers can't employ sloppy maths to drudgery around it. 1/0 would therefore be better represented as 1/(1/inf)=inf perhaps they could absorb a fresh symbols such as Q to reprsent the infinitely little and employ 0 to picture nothing or "no number". Thus div by zero would be x/q=inf

MaxI contemplate fraction of the problem arises due to the pass zero (0) is used alternately to picture void (nothing) or the infinitely little 1/inf. Void isn't 1/inf, void (0) would be more appropriately linked to "Not a Number" (NAN). The infinitely little soundless has size and illimitable progressions never achieve zero. It's always puzzled me how slack mathematicians are when considering stuff enjoy this. Far from being rare probs enjoy this crop up sum the time in computing and programmers can't employ sloppy maths to drudgery around it. 1/0 would therefore be better represented as 1/(1/inf)=inf perhaps they could absorb a fresh symbols such as Q to reprsent the infinitely little and employ 0 to picture nothing or "no number". Thus div by zero would be x/q=inf

KevinQuestion. What's so difficult about the thought that 0 divided 0 times is soundless 0? 1 divided zero times is 1? 2 divided zero times is 2? This is division right? That or if it's fractional the reply is always 0. Is that where this all bit comes in? -Kevin

josephi erudite that myself when i was 8 thanks!

SocratesBah. This is ridiculous. Why not just sigh that 1/0 equals infinity and proceed from there? You know, enjoy mathematicians accomplish sum THE TIME? The only problem that leaves is 0/0, and you only Get that in places enjoy uncanny limits, in which case math has more than enough fancy tricks to retreat around (like LaPlace's theorem). And that nullity symbol is just a capital phi. Not very inventive. Also, I would enjoy to situation for the record that anybody who can sigh "Imagine you're landing ON an aeroplane..." with a straight puss should not be teaching anybody any sort of high-level math. Not to mention the fact that even Bush isn't stupid enough to respect the possibilty of a pacemaker dividing by zero.

sylThe CS field already has a designated pass of referring to what you Get from dividing by zero - floating point has a defined NaN - NOT A NUMBER. You cant discharge any arithmetic on Not a Number. If you COULD discharge arithmetic on it, it would be picayune to "prove" that sum numbers are equal to sum other numbers - its a common mathematical brainteaser to give a chain of expressions that ends with " 1 = 0 ", with one of the steps being cleverly disguised division by 0. contemplate of it, you absorb six apples, and you need to divide by two - you divide the apples into two groups (of three) Even on this simple explanation, if you were to divide by zero, you'd need to divide the apples into zero groups. It doesnt stand for anything.

BertProfessor B. and Hmmm your both right. It is the lamest theory and in programming they accomplish absorb that exception handling to deal with problems that may antecedent things to crash... I contemplate this guy just want to Get into the advice and be seen... So he will invent any solution to problem or theory that would give five minutes of fame. As for teaching school children with lame theory as this nullity is stupid.

Blueit just sounds enjoy there giving something a designation rather than just motto it's an unknown factor...

WinjaThe biggest evidence that this has no mathematical basis is that 0/0 is different from any other true number divided by 0. 0/0 is not undefined. It is indeterminate. As an undergraduate math student, I absorb solved 0/0 in several problems. Sometimes it's undefined, sometimes it's 3, sometimes it's e, sometimes it's infinity...it can be anything. If I can understand this as an undergraduate student, I worry about how he received his doctorate.

2=1Wow...slow advice day huh. This is absolutely absurd. This is similar to that silly 2=1 proof that gets whored around the net. Zeros cannot simply be cancelled out.

FaroukI contemplate this thought is very interesting. Why? Because they need ideas to redefine the basics of their scholarship to unravel and cover more problems. Their goal is to unravel more problems. When this thought helped to unravel some unsolved problems, then you may contemplate that this thought may be the sole luminous thought of the century or even the millenium?! However, it is to soon to arbitrator that :)

Poly EsterSo you establish a symbol for undefined. You're soooo clever!

svThis is just pointless. Dr. Andersen is just making a mute "new number" that will change many things for the worse. It will fabricate programs harder to write because they now absorb to know when nullilty will be used. Its a nice idea, but not thought though enough. Anyways, the onlypeople who will understand this without complaining are students who havent heard about this topic yet. For everyone else, it will fuddle you even more. i contemplate that this is the dumbest thing that ever happened to the world of mathematics. Its enjoy changing the word mathematics to hahehahe. It confuses and makes no point. One more thing, what is that fraction about "nullity", being in a fresh number line, that must absorb been a shrimp kids's thought.

Nicolas CapensI've read parts of Dr. Anderson's articles now, and my biggest gripe is that he doesn't really unravel anything. Certainly not division by zero. He redefines 'undefined' to prove that the undefined of 0^0 is the same as the undefined of 0/0. I believe this is revise (at least in his algebra), but it doesn't really aid us. Airplanes will soundless crash when dividing by zero without handling the exception. I propound a number Q^-1 that is defined as the number you absorb to multiply 0 with to Get 1 (just enjoy the imaginary i is the number you absorb to multiply by itself to Get -1). Just enjoy i solves the problem of working with the square root of negative numbers, in practical situations, Q^-1 solves the problem of working with the division by 0. Also, i is physically mindless unless you multiply it with i to give -1, and Q^-1 is mindless unless it's multiplied by 0 (which is equal to Q, Q^-1's reciproke) to give 1. The most vital axioms: a = a*Q^0. a*Q^z / b*Q^w = (a/b)*Q^(z-w) {b !=0}, a*Q^(z-w-1) {b=0}. a*Q^z * b*Q^w = (a*b)*Q^(z*w). a*Q^z + b*Q^z = (a+b)*Q^z. Applying it to 0 / 0 gives 0*Q^-1. So that multiplication by 0 gives 0. Because Q is orthogonal to i they can actually define a three-dimensional space. For illustration the square root of -1/0 would be (0+1*i)*Q^-0.5. 0^0 does not appear to be 0*Q^-1 though...

Edward CherlinNaN has been a feature of IEEE floating point arithmetic for 20 years. Before that, the non-values Bottom and Nil were used in Computer Science for sum functions that didn't absorb proper values. The true number line and complex plane absorb been extended for well over a century with an illimitable value which makes them topologically complete, and Conway numbers can handle arithmetic on infinitesimals of sum orders. Alternatively a plane can be extended with a line at infinity, as in projective geometry, and sum of the points at infinity can be represented in homogeneous coordinates using only finite numbers--the sort of thing your graphics card has to accomplish to manage the patent meeting point of parallel lines. Painters erudite to fabricate lines at infinity drudgery back in the Renaissance. You can examine sum of this stuff up on Wikipedia. So this is picayune and not advice at sum to artists, hackers, or mathematicians.

Rick BurginI would've discovered this a long time ago if I'd absorb realised I could create my own number outside the "conventional number line". It's enjoy playing a game and making your own rules up as you retreat along. What a failure.

DustinWhay cant they focus on curing cancer instead of making up numbers? Seems to me to be a better employ of their time.

Nicolas CapensCorrection to my previous post: Numbers can't be both a division of zero and a multiple of zero at the same time, so only one bit field suffices. I besides absorb a better notation: Lets write 5(/0) as 5*Q^-1 and 3(*0) as 3*Q^1. And define Q^0 as 1. So it's an algebraic remonstrate enjoy the imaginary i. So in their binary representation they only absorb to store the exponent of Q. true numbers absorb a Q exponent 0. Divisions by zero absorb an negative Q exponent. Multiples of zero absorb a positive Q exponent. With just two bits they could avert up to double division by zero exceptions. © 2006 Nicolas Capens

TurkutomI believe there is one employ for the term of nullity. Nullity equals Dr. Anderson's IQ divided by the product of Dr. Anderson's supporters. That being said, I conform with the comments made by the majority of the responders. Nullity is merely a fresh word to sigh that it is either undefined or defined as itself.

Nicolas CapensThis approach has only (limited) employ in computer science. sigh they need to compute a * b, but an external library only gives us a / x. So they absorb to multiply with b * x, but if x = 0 then they Get NaN and not a * b. The solution is to withhold the numerator when dividing by zero, and set a bit that indicates division by zero. sigh a = 5 then they could write 5 / 0 = 5(/0). besides when multiplying by zero they withhold the original value but set a bit that indicated multiplicatio by zero. sigh b = 3 then they could write 3 * 0 = 3(*0). When multiplying a and b they Get 5(/0) * 3(*0) = 15. The (/0) and (*0) bits cancel each other. So basically 0 / 0 is soundless undefined, but (a / x) * (b * x) is defined as a * b. Obviously, this doesn't really unravel anything, because the software should be able to compute a * b directly. A well designed external library has to provide a separately as well. It can effectively avoid division by zero crahes in badly written software though. But it soundless has its practical limits. If they absorb (a / x / y) * (b * x * y) then they need extra bits to indicate double division by zero and double multiplication by zero (four bits actually suffice for up to triple division and multiplication by zero). Even if they add those there would soundless be an exception and a potential crash when dividing by zero four times... © 2006 Nicolas Capens :-)

Jonesi contemplate that this is pointless

Professor B.This has to be the sole most lamest theory so far this millennium.

Hmm""Imagine you're landing on an aeroplane and the automatic pilot's working," he suggests. "If it divides by zero and the computer stops working - you're in broad trouble. If your heart pacemaker divides by zero, you're dead."" It's called exception handling...

jaclexWell, complex numbers were not considered before but now they contemplate its application in the true world. So, let's find out if the theory about nullity can pass the mathematical community. Thus, how will they convoke this fresh set of numbers (with nullity)?

Arnold SchmidtTo contemplate the failure of Western citizens to achieve any degree of basic mathematical literacy, examine no further than this idiotic piece of "journalism." "Dr." Anderson's "nullity" symbol is neither theory nor discovery; it is merely a publicity stunt by a hapless "professor" who realized that BBC reporters are, to reclaim it mildly, dumb. This article is an embarassment to the mathematical community everywhere.

JKSit sounds enjoy he's suggesting that dividing by zero leaves you with a value that represents the set of sum numbers from -inf to +inf... IE: infinity. They already knew that dividing by zero left us (basically) with infinity. This is fairly stupid.

The prudent ManAn infinitely null thought amounting to nothing.

JeffIt seems that people are very content to designation something, thinking it will help. But it's just a convenient tool that doesn't retreat anywhere. Until I contemplate where it is useful, where this fresh symbol holds any more meaning than 0/0, then I'm not convinced.

roy bobI heard that miscrosoft is running a fresh service pack to update their OS. - if they knew this theory a year before most of their security updates would fabricate nosense. This is the desmonstration that they where right, their software is the best, but they couldn't manage what they don't know. sum their programmers are older than 16, so they know nothing about nullity. Intell is now working with apple to unravel the problem in future versions of their processor. - They are really timid about implications: they are soundless evaluating how far accomplish they absorb to retreat developing a fresh ALU for this. So we'll know much more in the future.

nullityThis is me, I got solved. btw, the problem is not this theory, solving an inexistent problem.. They allow a stupid operation, divide 'nothing' into 'something'. I recollect I was told to accomplish NOT add 'pears' and 'apples' because "it can't be done". Lets retreat further, avoid any mathematical theory regarding "0 divided by", just because it can't be done. For now lets designation this brand fresh theory the "End Point theory". Whenever you find the "0 divided by" patter, stop, as it can't be done. mm better if retreat one step further, Lets doubt the axioms of the actual theory: Instead of trying to unravel the solution 0/x, respect the problem this kindhearted of situations, "if this pass leads you to 0/x, then your pass is wrong from the beginning", don't gyrate the solution a fresh problem. I'm the only one who thinks that maths where created and can besides be changed? or they soundless must to thank god for this?

Dr Charles AllerstonThe length of this thread clearly proves that infinity exists.

AniketI contemplate 0/0=nullity="Nonsense!"

Uncle DaveI adore this. Using nullity I can now complete my design for a perpetual motion machine. Patent Office here I come!

PointlessNullity solves nothing. It's a fresh pass to accomplish the same thing- that is, nothing. Nullity soundless can't be manipulated into any shape of employ other than the uses other concepts absorb fulfilled via calculus equations. He's just trying to fabricate it appear enjoy he invented something, when he just reworded it in essence. And shame on the BBC. I always thought they were smarter than to actually publish something enjoy this.

seymore butswell if you had 2 apples and reclaim them into 0 groups then there wouldnt be any apples because there is no group to reclaim them into right? that simple...

Tomek PerlakRe: a physics proof --- But haven't you just proven that the first equation does not 'always' apply, hence a better one, including both the mass and the frequency should be applied? --- Please, note, this is said from a 'mere mortal' point of view --- and yet, what you've said could point to a conclusion that mass and frequency are not really two different concepts, but more so two different 'interfaces' to the energy in matter? --- Anyways, if there are two equation in employ for energy, I would besides 'allow' for two different cases with 'nullity' in them; just a thought;

Jason DickThe stupid thing about this is that mathematicians absorb been dividing by zero for quite some time. It's basically a requirement to accomplish any calculus. The concept of nullity adds exactly nothing whatsoever to mathematics: they already absorb well-defined concepts for how to deal with division by zero. This is, essentially, the same as somebody declaring that he or she knows how to seize the square root of -2, calling it negativity or some such.

Interesting, but...Nothing from Nothing Leaves Nothing! Billy Preston 1974

EngineerThis is the most pointless BBC article since "Sudan Man ordered to Marry Goat". I feel terribly sorry for any of his pupils, that upon taking maths above GCSE will find that their genius of a teacher has in fact taught them total rubbish. And of course the fact that Transreal Computing Ltd requires publicity has nothing to accomplish with this ridiculous claim.

Nikolas BourbakiI find the results very interesting, after having read the explanation on Wikipedia. gratify read further before going too crazy, he is working with "transreals", not the true number system. Perhaps it would be better if he besides invented a fresh symbol for his trasreal zero, unless his zero is real, I'm not positive what the case is. Oh well, I contemplate I'll retreat sharpen some pencils demurely and give my sliderule a wipedown before retiring to the library.

DanPerhaps this is a safe time for me to argue my own recently published research. 1.9999... repeating is "pseudo2". In every respect it is enjoy the number 2 except that the result of arithmetic operations using pseudo2 are decremented by 1 and added to 0.9999... repeating. This brings me to my next research topic called "pseudo1" which I am currently working on, but sum I will sigh for now is that it requires a radically different seize on how they contemplate mathematics and could absorb revolutionary benefits for computing. If you don't believe me I'd be delighted to present you working protoype applications demonstrating my research.

Christopher JoyceI'm confused? transreal arithmetic states that ln[-1]={PHI} where as complex arithmetic states that ln[-1]=i{PI}; so while transreal arithmetic considers ln[-1] to be nullity (and not complex), complex arithmetic considers ln[-1] to be complex (and not nullity), so aren't transreal and complex arithmetic inconsistent?

Joe BarkunI didn't really understand the true employ for this "new" theory... And could you gratify employ it in a analytic MATHMATICAL equation or application...

tutti"sits outside the conventional number line"... in other words, it isn't a number? That's cute.

Mikei don't contemplate what the distinguished point is though, it needs purpose. dividing nothing into no equal groups (aka 0/0) i don't contemplate will accomplish us any good. with the lack of value divided by the lack of value your not getting anything substantial and to any power except maybe the zeroeth power it remains the same. If there will be a employ for it i really hope i Get to contemplate it. And no uses are stated although it says it has use. "Make sum kinds of sums possible"

Darrenyou accomplish realize that if this is honest then 2 now equals 1. contemplate this proof: assume a=b so starting: 1.a=b 2.aa=ab 3.aa-bb=ab-bb 4.(a-b)(a+b)=b(a-b) 5.a+b=b 6.2b=b 7.2=1 the only thing keeping this from being honest is step 4 to step 5... division by (a-b). since a=b then a-b=0, and division by zero making the proof false. he just made 1=2... yeah absorb fun with math now... when 1+1={1,1.5,2,3,4}

AimeeNullity seems no better to me than undefined... what's it equal to? How accomplish you employ it in sums? Where does it felicitous on the number line? Does it need a different axis, enjoy i? I need a safe definition, then I'll contemplate about it.

Karl BabbittWhy not accept that YOU CAN'T DEVIDE BY 0!? Nullity is a very despicable idea, looks enjoy a caveman came up with the symbol.

Rainer Raisch, Munich, Germanymultiplying with zero always gives the result zero. Its not reversible enjoy infinity as result of the division x/0. This "problem" needs no cure.

bdIt's limpid that this had to arrive from a computer "scientist". Any secone-year math student would seize it apart within seconds. I just prodigy how BBC fell for that nonsense, I thought higher of them.

DevildogTo be a safe theory, a scientific theory must among others be relevant to real-world problem solving. Other from that, I must sigh it's an veneration to absorb Mr. Norris comment on this page. Thank you.

JonAxioms 19 and 20 are troubling (bijectivity of reciprocal and 1/0 = infinity). Doesn't sit well with calculus.

Arturo MartinezDr. Anderson: Axiom 16 (NULL=Inf*0) is not at axiom at all, check: NULL=-NULL -> A9 1*(0/0)=-NULL -> Definition of Nullity 0*(1/0)=-NULL -> A13 0*INF=-NULL -> Definition of Infinity in R^t 0*INF=NULL -> A9 I'm soundless not positive if R^t can build a consistent algebra

Richard R.This is perhaps the stupidest thing I've ever heard. I am led to believe that neither Anderson nor the journalist of this article possess a mathematics proficiency higher than these students who are being lied to.

Braindead DanWell, shouldn't 0^0 = 1? Because 0 divides into itself once, enjoy any number divided by itself 1^1 = 1, 2^2 = 1, etc... Just my thoughts.

Jorian HooverI contemplate I've got it. This "nullity" is prety much the same as undefined, but easier to express on paper. I prodigy how lickety-split this will spread around. -Jorian Hoover

Zach M.Being a senior in lofty school, I contemplate this and think, "Well, I won't absorb to worry about this." Then I realize I'm about to head into college. Well, now that I've heard of the concept, at least I can mentally prepare myself for it. And if this keeps up, I'll just absorb to withhold myself mentally prepared when they rush out of note variables and start using animals.

Bob BinkmanI find it quite entertaining how Pythagoras got to drudgery on a 1200-year traditional problem more than 2000 years ago. :)

Vader PietIf you guys enjoy true math about infinity, gratify read the book: "The Mystery of the Aleph: Mathematics, the Kabbalah, and the Human Mind" or just search for Georg Cantor and why he spent his terminal hours in a mental institute.

Victor*LOL* I contemplate people should be less mad at Mr Andersen and direct their deride at BBC for running such a hilarious article. Bravo BBC, you're competing with the tabloids for the trait of reporting. Any nascence calculus student knows that the concept of a circumscribe resolved the division by zero problem ages ago. The fact that computer returns an error does not stand for there is a problem - it simply means that it is incompetent to employ the computer output without thinking about the round-off issues and the like. Millions of professionals employ existing algebra to calculate anything from portfolio allocations to space shuttle trajectories, and I can assure you that any future Mars expedition won't miss its orbit for the want of nullity in its computer system.

Caoltan Strainstupid. doesn't prove anything/ fabricate anything any better. its still, in reality, undefined

Jimmy JohnsAccording to Jake`s theorem, when Nullity is plugged into the quadratic formula, they find that Nullity is obviously equal to (1-C). Therefore, (1-c)^2-(1-c)+C = 0; And in effect C=0. Thus proving that nullity equals (1-c), or 1.

Sara PostmaYou are my hero!!! i adore you!!!!!!

WoxorThis might be useful for pedagogical purposes, since it's often uncomfortable for students to learn that some things simply "don't exist" (like 1/0), but it has very shrimp scientific value. Computer programs soundless can't divide by zero, but they drudgery around that by handling those sorts of exceptions. This is just another pass of handling the exception, so to speak. From a unadulterated math standpoint, I'm unafraid it's completely useless since the addition of nullity to the reals would withhold it from being a field, or even a ring (0/0 * 0/1 = 0/0, but a*0 =0 for sum a in a ring), so multiplication would fail. And without multiplication, there's no need for 0/0 because it requires the concept of division. From a topological standpoint, it's already been done, since 1/0 is treated as infinity in many ways when constructing complex conformal maps, for example. It's besides a bit native to feign that this has even been a problem, that it has been a problem for 1200 years, and that some guy just came along and solved it with the mathematical equivalent of rewording the problem. It seems the best quantitative description of the worth of this suppositious discovery is nullity itself.

Gregory C.Maybe Dr. Anderson's brain tried to divide by zero.

David NI suppose everything would be just fine if your pacemaker tells you that your next hearbeat should be in nullity milliseconds instead. This theory is neither revolutionary nor useful. No-one should be taught mathematics by someone who marks plus and minus infinity with dots on the true number line.

Nurse DragonbreathI believe Ray Lashley (way down the list) comes closest to the solution of this mystery. BBC is "pulling their legs". They wave this 'Crazy Doctor' with his flawed math in front of us in order to excite reactions. And they retreat straight into the trap! I'm not positive it was BBC, but I'm positive it was some Brittish channel which, a few years ago, aired a kindhearted of 'game show' having people who slept on the streets as participants. The contesters were made to accomplish various humiliating tasks enjoy trying to build shelters from cardbord boxes and other junk. Those who did not win (in what appeared to be a very unfairly judged contest) had to retreat back to the streets with next to nothing. This provoked an outrage from viewers who phoned and wrote to the TV station motto 'you can't accomplish this to people' etc. Actually, it was sum a scam, aimed exactly at provoking this kindhearted of reaction. It felt safe then to contemplate that people reacted against the 'game show', and (since I wager this is a similar case) it's safe now to contemplate that people really supervision so deeply about math. And by the way; I contemplate I solved these math issues terminal night, if you just supervision to read on. What they want is a definition of the circumscribe 1/x as x approaches zero (currently math defines this value as NOT limited, but rather as 'growing without bounds' iow NOT existing, iow indeterminate. But I absorb the solution! let x and y be capricious postive reals, so that y

Mathew PeetZero divided by Zero should be a number on the number line. It has to equivocate somewhere between minus infinity and infinity, (including 0). For approximate values of 0 perhaps there are solutions. For true 0 the reply has to equivocate everywhere. It would be more useful to contemplate of the reply as 0 +/- infinity. Or indeterminate. Thanks for this legend it was useful mental exercise :)

papersnowmanI conform with Rob. Debating and deciding whether or not this theory is an vital task, but more importantly, why is a theory that hasn't been fully proven/reviewed being taught to their children? If this theory proves to be wrong, would you enjoy to know that your children will never understand higher smooth mathematics because they had this theory inbedded into them at such a puerile age? Also, at these ages, children seize information enjoy this as unadulterated 100% undeniable fact without much secondguessing at all, by the time this is proven one pass or the other for sure, it will be ingrained in their heads too deeply to remove, for most of them. -- Papersnowman

BobAnyone who has even just completed basic programming knows about "null" and thus this is not a breakthrough.

MichaelThis is weird. This is not dividing by zero, it's just enjoy motto 0/0=x. X could be anything. I'm a sixth grader in the US, and this is just plain stupid, even though I don't understand the comments above I can contemplate that they point to nullity being inconsistent. Setting a variable for 0/0 is suppositious to be revolutionary? I contemplate not!

ericwow. this journalist should learn more about a topic before reporting on it. he/she acted enjoy dividing by zero could actually work. "nullity" wouldn't drudgery because its not consistent

Nick>>"Right or wrong, it always surprises me how many people are willing to be pretty nasty to someone who's arrive up with a different pass of thinking. Why is it so personal to people? Why accomplish people insist the other person is stupid?" The reason it angers people is because Dr. Anderson didn't even try to prove the consistency of his number system, let solitary Get it published in a reputable math journal. He just contacted the press to Get his 15 minutes of fame. This is very frustrating for people trying to accomplish true mathematics, who absorb published extensive articles on why this makes no sense and yet Get no attention whatsoever from common people. Now mathematicians laugh at him (and rightfully so), which just reinforces the layman viewpoint that science is a broad conspiracy that rejects criticism and alternative theories. Yes, mathematicians are perfectly birthright to be mad and to seize it personally. If he wants to be taken seriously, he should publish a paper on it before teaching it to a bunch of grade schoolers.

MatthewWrong, his "solution" is enjoy saying: one can Get to the other side of the universe by going faster than the speen of light. It's nice to say, but doesn't stand for anything at all.

A. CummingsI'd enjoy to point out that 1 divided by 0 is not infinity. Dividing by 0 is actually an illogical expression because 0 doesn't absorb a value. For a division expression to be mathematically analytic the denominator needs to absorb a value.

GiorgosIf professor can explain to us sum what is the fresh number then yes he solved the problem. Until then the only contemplate he proved is than the 0 in the power of 0 equals with 0 divided by zero.

endloserSo... if I am looking at this right... zero is nothing... it is already just a status holder. You really can't multiply by zero because you had nothing to start with. Just enjoy you can't divide, because you had nothing to start with. If you assume that one of nothing is nothing, then no parts of something is nothing. There I divided by zero. Not infinite. Just not existant. Maybe the reply isn't dividing by zero but getting rid of the status holder and embracing the nothingness. And how to picture nothing? With nothing. Just a thought... one that got me detention in grade school for being "insubordinate".

AySz88One of the *first* things he does on that whiteboard is wrong: 1/0 is not and should not be defined as infinity. It can be either infinity or negative infinity. Graphing f(x) = 1/x makes this obvious, or you can try this: respect 1/x. Let x be a positive number, and shrink it towards zero. This is enjoy approaching x=0 on the aforementioned graph from the birthright side. The result grows towards infinity. Now let x be a *negative* number. Now 1/x approaches *negative* infinity! 1/0 can be considered either infinity or negative infinity, depending on what the math is being applied to.

l.schatzHe is introducing a fresh element and he doesn't even define a fresh set. He uses multiplication of the traditional set without prooving he can employ it. I prodigy if he proove the possiblity to introduce this element or if he just employ it without thinking of consequences at all? poverty-stricken pupils if he train such theories without prooving them!

Oxford Mathematics MScJeremy Lundy, it is not incongruous to absorb nullity = e^(-nullity) in this model. seize for illustration the fact that a*infinity = infinity when a is a true number. This does not prove infinity is incongruous when infinity is defined in the pass by Anderson here. besides contemplate about a*0 = 0. I very much doubt whether nullity is going to be of any use, but the mathematics doesn't appear to be incongruous to me.

BradMany of the education majors I went to college with were in Remedial Math. Apparently some of these absorb developed their own mathematical style. But if giving a particular kindhearted of indeterminism a designation proves to be a useful pedagogical crutch, why not?

DoctorbDr. Anderson motto that 0/0 is a number is enjoy motto that an egg is a number. Would he enjoy to define what he means by a number?

Pennywise the ClownTwo things: The theorem T81 [(a*b)^-1=a^-1*b^-1 : a=/=0 and b=/=neg] needs to be an axiom, because the axioms don't appear to warrant the guarding clause. Plus, this means that before, division by zero was not allowed, now with division by x*0, x negative, I can't employ T81. What's the broad gain? It seems this only complicates things.

ED?As a 2nd year maths student I was very excited to hear about the possibility of dividing by zero. But it turns out that is not what's happening at all. Now I am disapointed, but my heart warmed to contemplate so many people pointing out sum the flaws so I don't absorb to.

Andy L.Since Dr.Anderson will be answering questions later today, here's my first question. 1) Given that the even Gentzen's system for his consistency proof for Peano Arithmetic is itself not been proven consistent, how can you be positive that the Essex Dr.'s mechanical proof of the consistency of your system is anything but hotair?

Matthew HareRight or wrong, it always surprises me how many people are willing to be pretty nasty to someone who's arrive up with a different pass of thinking. Why is it so personal to people? Why accomplish people insist the other person is stupid? He's either birthright or wrong, or he's birthright in a positive field, and wrong in another field. But accomplish people actually need to Get personal about it? Who are they? Are they distinguished minds? Or accomplish they just contemplate they are distinguished minds?

AndrewWhat's wrong with creating a fresh concept of Nullity? It may aid out enjoy "i" did (imaginary numbers, sqrt(-1), etc.) in the understanding of previously unsolvable concepts.

GeorgeI really contemplate that this fresh theory may actually aid people and reclaim alot of money, time, and even lives. besides I absorb seen alot of negative feedback from people just because they dont understand the thought and they contemplate its preposterous. Open your minds. You should at least give Dr. Anderson a casual and comment on it later on.

Jeremy LundyUsing his defintion here is a proof that shows nullity isnt consistent: Assume to the contrary nullity is consitent. Let x=0^0 = nullity lnx = ln(0^0) lnx = 0*ln(0) lnx = 0*(-infinity) (since its a point be his definition) lnx = 0*(-1/0) lnx = (0/0)*-1 lnx = nullity * -1 x = e^(-nullity) Hence: nullity = e^(-nullity) This is a contradiction. Hence nullity isnt consistent.

AnonMSo, lim(x->1) (x-1)/lnx can be evaluated using L'Hopital's. It yeilds 1. Or, if you don't know L'hopital's, examine at a graphing calculator and find the circumscribe of the function as x->1. But, by direct substition in the circumscribe they Get 0/0 (one of the indeterminate forms for L'Hopital's), so the circumscribe would be the nullity symbol- no need to apply L'Hopital's if they absorb the "number" by direct substitution. As math should be consistent, apply the transitive property. They now absorb that "nullity" = 1. Well, it equals 1 for THIS problem, they could, of course, fabricate it equal any number of their choosing by changing the circumscribe problem (multiply the x in the numerator by your favorite number). Or, respect the structure of division related back to multiplication [6/2=3 because 2*3=6]. If they accomplish this for 0/0 they absorb the following: 0/0=? becomes 0*?=0. Any number could be filled into the question note (which is why undefined is an appropriate response to 0/0). Thus, if they are to absorb a word or symbol for 0/0 or 0^0 [the same thing by exponent rules- which is why they absorb a^0=1, if a==0] then "nullity" isn't a safe one. It should be "everythingy".

T. VukI conform with Dr Noisewater.

cameronhow is calling 0/0 "nullity" any more useful than simply motto it is undefined?

CurtIndeed, he's besides making the assumption that sum infinities are equal.

Andy BI had him as a lecturer for computer graphics, and he explained this to us. I followed what he said and came to conform with him that something divided by zero is not "on the number line". broad deal. Computer Science, and many programming languages, already employ NaN - Not A Number. Heck, I didn't contemplate Infinity was a number either - certainly, I can't picture it as a binary number... Also, having just arrive from a Control Theory lecture I was annoyed by the all 'number line' industry - every Cybernetics undergrad knows you can't really absorb numbers without imaginary numbers - so it's sum a plane anyway. ;op Still, some of the abuse here is unwarranted - I thought he was one of the better Comp Sci lecturers, and clearly very bright. enjoy some comments say, though, I did contemplate 'big deal', and he isn't a mathematician.

s squaredIf Dr. Anderson is reading these comments: I would enjoy him to complicated on how his system differs from IEEE flaoting point standard's NaN, +infinity and -infinity.

X37VI don't really contemplate they can accomplish anything with 'nullity' yet. It's just another name, really. But what is useful is the thought of numbers off the number line. If they can figure out more nubers enjoy this, maybe they will discontinuance up finding a all fresh number line, and find out how to actually employ 0/0. It's the concept, not the current usefullness, that's important.

Shanna WilcoxSo I can contemplate where he's coming from. Technically they accomplish not know an exact value for infinity, but when you devide by infinity you Get the approximate value of zero. Therefore I am nascence to believe that if you devide by zero, "nullity" you would Get the approximate value of infinity. That just makes sense to me...

Bill GoughVery entertaining the smooth of inflame generated by a useful idea. They certainly know from family dinners how much insecurity (or its mirror image - smugness) determines a matching smooth of anger. I've read postings suggesting that a thinker be 'flogged' and others dismissing postings because of 'language' This fresh symbol, no matter what its application in math, is proving to be a fine generator of class-bias and racism. Hmmmm - might be something to this concept.

James LaniganI am an aerospace engineer and I conform fully with his theory. You guys don't know the history of math. You just believe what the math community wants you to. I know the history of math. Now if Gene Simmons was teaching this, I would believe it.

LukeDr. Anderson wrote a reply waay down somewhere explaining that he has formally axiomatized trans-real arithmetic, and that it has been proved consistent. While it is simple to arrive up with contradictions using Nullity and ordinary arithmetic, I am interested to contemplate his axioms. It may not be an incredible discovery, it may be an entertaining system to drudgery in if it is consistent. gratify give details.

Dr. LimeyToo complicated to train the all world this fresh theory. They should ignore it.

ReidMost of the posts here are just stating the incorrectness of Dr. Anderson's work, but zilch of them give a truly rigorous proof of the inconsistencies. Due to Dr. Anderson's agreement to comment on the criticisms of his theory of 'nullity', I thought that I'd give such a proof for him to comment on. Hopefully, the BBC will retain the formatting of my post as it will probably be difficult to read without the necessary white-space. They start with some definitions. In the video provided by the BBC, Dr. Anderson gives the definition of infinity to be 1/0. In a post on this article, someone posted as Dr. Anderson (I will assume here that this is actually Dr. Anderson) and had this to sigh (he implies this in the video as well): "It is just an arithmetical fact that 1/0 is the biggest number there is." So, to reclaim this in rigorous mathematical language, they absorb the following from Dr. Anderson: 1) infinity = 1/0 2) infinity is an element of the true Numbers (hereafter denoted R) 3) R is bounded above by infinity They besides know that R is a field and 1 is an element of R. To present that Dr. Anderson's proof is fallacious, they will present that one of his base definitions (infinity) leads to a contradiction. Let infinity be defined as in 1), 2) and 3). It is besides given that R is a field with 1 an element of R. From the axioms of a field they know that for every a and b in R, a + b is in R as well. Thus, infinity + 1 is in R. But, by the habitual ordering of R, they have: infinity

Steve JayOnce upon a time they had no number zero, then the Moors showed the Romans the fresh number they'd invented, and book keeping break-evens got a lot easier. This is no more controversial than that, really.

Edgar MatiasThis problem was solved in the 1960s by Abraham Robinson, a Mathematician and Logician. Using mathematical logic, he proved that you could extend Calculus to included "infinities" and "infinitesimals". He called it Non-Standard Analysis (Google it/him for more info). Basically, he defined a set of numbers called Hyper-Real numbers, that included sum true numbers + infinities + infinitesimals. Any honest statement using Hyper-Real numbers is besides honest using true numbers, so long as the infinities and infinitesimals cancelled each other out in the final answer. So, instead of dividing by zero, you divide by an infinitesimal number. You accomplish sum of your equation manipulation this way, and as long as the final reply isn't illimitable or infinitesimal, everything is fine. It's a shame more people don't know about this. Much of basic Calculus was originally invented using reasoning similar to Robinson's. His drudgery just legitimized those approaches, making them sound proofs.

LazzerIt is incredible that the true problem with infinities is not even discussed. The result of division by zero is not a simple number. Why? When you divide by zero you delete information. Precisely you delete the information what was divided. sum numbers devided by zero result in infinity. The problems start applying equality to infinities. In almost sum cases this is not correct, because infinity simply has no identity. One infinity in not the same enjoy the next infinity. Undefined is not wrong, but it goes to far because you can soundless determine attributes from the infinity e.g. when the infinity result from dividing a number by zero the resulting infinity besides has the nature of a number even if it is not finit. Try to approximate the division by zero dividing with numbers enjoy 0.1, 0.01, 0.001, 0.0001 and so on. If you devide the numbers 1 and 2 this way, you notice the result growing. The equations are 1 / n and 2 / n. It is limpid that (2 / n) / (1 / n) results in 2. But using infinity you cannot sigh 1 / 0 = infinity and 2 / n = infinity. But infinity / infinity must not result in 2 because it has less information than the source if the infinity. The quotient of such infinities must be a number, but you accomplish not know which. Unknown numbers are represented by variables, normally. You besides can picture infinites by variables to distinquish them. Using phi for a number ist just a variable without a useful name. You're unable to reference that number. Maybe in some cases you accomplish not need a reference. But you besides absorb no further capitalize for your calculations.

Brian FantanaSorry about my dangling friend's assorted rambling, but Dr Noisewater is very difficult to withhold pacified these days.

S SquaredYou write that Dr. Anderson will reply questions about his theory of 'nullity' on Tuesday. If so, and he reads this comment, can he gratify retreat into more detail about how his system differs from the IEEE floating point standard's NaN (Not a Number), +infinity and -infinity.

Dr Kenneth NoisewaterI would enjoy to know why he didn't present this 'solution' to some lofty smooth Math students. Oh, but I already know the answer, because they actually understand complex mathmatics. This doesn't unravel anything programming wise, you might as well assume that 'nullity' is synonymous with 'error'. If you're dividing by zero in computing, you're generally doing something wrong. What exactly are computers suppositious to accomplish with 'nullity', and where are it's practical uses, other than another designation for something that is undefined.

ChristopherOk first, one cannot define infinity = 1/0 because 1/0 is undefined (and dividing by zero is what he's here to define). What infinity can be defined as is: infinity = 1/n as n approaches zero But fine, they can pass that up. In his proof, he has: 0^0 = 0^(1-1) 0^0 = (0/1)^1 * (0/1)^(-1) 0^0 = (0/1)^1 * (1/0)^1 desist birthright there, he has an indeterminate form, 1/0 is undefined, this line in the proof has to be honest in order for the result to be true. But, he gets around this because he has defined 1/0 = infinity, which is sum kinds of wrong.

FigsThis is why they absorb try{} constructions. Why would 'nullity' be useful? I contemplate no reason that nullity would be better than NaN.

BartBThere was a rumour that a U.S. situation in law defined PI = 3.0 Such definition, fortunately, did not fabricate it so.

TelanisThis is a silly idea. Computers cannot handle "nullity" any more than they can handle "N/A" for 0/0. error checking will not be replaced, it will simply be misnamed, and more errors will arrive as a result.

SylvaniaI absolutely understand it. When will this be taught in schools around the world. It fills a large gap of understanding when studying Calc.

DarmokWhat? Is this satire? If so, it should be clearly indicated instead of presenting this as some sort of credible concept. And if not, is there no one at the BBC confidential with mathematics who can review these stories? Or at least contact an expert in the field or at least a local professor before publishing garbage enjoy this. BBC, you should be ashamed.

jackhey, some of you people bother me. how many of you absorb said "1/0 = infinity" here is why that is NOT true: 1 = 0∞ = (0+0)∞ = 0∞ + 0∞ = 1+1 = 2 see, it doesnt felicitous true math if 1 = 2 anyway, sum that this guy is doing is making a symbol for this indeterminate result. instead of just writing "not real" or "indeterminite" he decides to fabricate a shrimp symbol for it. as far as i absorb seen it has no implications beyond allowing computers to not freak out when one divides by zero

BlueRajaThis doesn't unravel any problem related to Computer Science... Computers don't inherently know how to divide (or accomplish anything, for that matter); they absorb to be taught - someone has to design the circuit for division, and figure out what to accomplish in the case of divisor=0. In most cases, an exception is thrown or an error flag is set; however, I've never heard of a system shutting off when dividing by zero (and I *highly* doubt they'd program a pacemaker or autopilot to shut-off in that case).

SymphosisJason, the reason 1 is the circumscribe is because its a definition; made up because it suited their purpose. dont contemplate your dispute is accurate, same for many other of you people. In any case, I am not positive Dr Anderson has actually given us anything they can actually implement.. but nice trying..

LizzI am joyous that BBC wrote about this. I never knew this was a problem, but by reading about Dr. Anderson's theory I establish the solution myself. And I am not going to divulge it here :-) Dr. Anderson's theory is wrong. That much I can sigh for sure.

AhmedI am an engineer .. i didn't understand what did Dr James Anderson came up with but it's something incredible !!

Ole-RoaldIn computer programming they seize hand of dividing by zero as a sunder event in where chain of calculations. How this event will be taken, will be decided by programmer during analyzing the environment in which the calculation serie is doing. As I know, the birthright decition will be done if division by zero occur. Therefore there is no occasion to be unafraid of something going wrong in autopilots in aircrafts, and in pacemakers.

JThere is nothing fresh here. What Dr. Anderson has done is to seize those operations, (in the reals or extended reals) which result in nonsense, (in the habitual sense) and employ them to define nullity, (specifically those cases which are not handled by the extended reals). To summarize, they now absorb a fresh word for undefined. P.S. What happened to the co-authors of Dr. Anderson's on this subject? (See the academic papers on the subject: Perspex Machine 8 & 9).

Ste Millington (Software engineer with unadulterated MathsWhat is the point of a computer happily churning away calculations involving division by zero without any errors only to find that the results don't absorb any meaning? I personally wouldn't enjoy to be on a plane operating with Dr Andersons fresh arithmetic when because of some programming error a division by zero occurs and the navigation system carries on regardless - giving us a position of nullity by nullity! Dr Andersons axiomatisation of his fresh number system does materialize to be consistent (given a cursory glance) however it's just plain useless! The point is that in the true world if you are trying to divide something by zero you absorb made a mistake and any well written computer program should handle these errors effortlessly. In Dr Andersons fresh system they gain the capacity to discharge division by any number upon any number, but at what cost? Well to start with they can no longer infer that because x + a = x + b then a = b. This is such an ingrained and natural notion that adopting the fresh number system would inevitably lead people to error. Though sickeningly grandiose in tone Dr Anderson's first paper does at first glance materialize at least to be consistent within in its own bounds. Fine. His second paper on calculus exposes a limpid lack of mathematical training and is flawed in many places. I would be amazed if any peer reviewed journal would respect publishing either paper.

Matt PThis looks about as useful as complex (or imaginary or non-real) numbers in that in conventional and most applications, it is entirely useless, a mathematical definition with shape and no subtance. (finishing year Calculus student)

Suspicious Cricket FanI am indeed very suspicious. It seems as if this all theory has been invented to howsoever apply some formula to the impending Australia 5 England 0 result in the Ashes Tests to provide a "mathematical" possibility of England retaining the Ashes despite sending out a second rate exotic legion XI who play enjoy crap.

Eric MillDr. Anderson should Get in palpate with Dr. Stephen Colbert, an equally renowned logician, whose concept of "truthiness" has been getting an incredible amount of press.

JenniferWe sum know that it's impossible to divide by 0... but is it impossible to MULTIPLY by 0?

p@Sorry, but could somebody gratify insitute a national programme to train people spelling and grammar? I realise some of the posters are not native English speakers, but the majority of the rest need to absorb something equivalent to national service to aid them learn to communicate. Once that is done, perhaps they could try learning some mathematics and, in many case, computer science.

Patrick DEMICHELOne of the most glowing illustration of the stupidity of the journalists. There are tons of true astonishing scientific breakthroughs that they never ear about because too difficult to understand for the quasi totality of pseudo scientific journalisms they contemplate on televisions and web and hear on radios. This non-problem is very picayune to demonstrate to pupils 0.001^0.001=0.9931 0.0001^0.0001=0.999079 0.00001^0.00001=0.99988 0.000001^0.000001=0.999986 Even non mathematicians contemplate this converge to 1 : then 0^0=1 This is not because your computer does not drudgery due to poorly implement code that you should contemplate that there is no solution. Why need to create absurd symbol for 1? gratify Please journalisms of the world, the best thing you can accomplish when you absorb nothing to write or sigh it to shut up and seize vacations, don't pollute their medias. One thing I can recognize here is : they are qualified to talk about nullity , even illimitable nullity :-) And to finish most processors know what to accomplish to divide by 0 , but the programmers need to pay attention to this detail and deal an interrupt or the Nan or illimitable number they will Get if they divide by 0

TuomasJason's resoning is faulty, as (1/x)^(1/x^2) goes to infinity as x->oo even though it approaches 0^0. The point of 0^0 in a calculation is "how" one is reaching the limit. The "nullity" has been around in computer science, most math processors absorb a special "number" NaN, which stands for Not a Number. The result of 0^0 is NaN, which this professor calls nullity. Nothing to contemplate here, inch along!

LukasI suppose this could open up fresh branches of abstract physics, but in practical application, it's pretty silly. soundless I suppose this is no worse then when 'i' was assigned the square root of negative one.

IanCan you define a word, by using that word in a definition?

TewAnd here I thought dividing by zero was infinity...

Jason0^0 is indeterminate, but if you seize (1/x)^(1/x) as x gets very large is essentially 0^0. However, this circumscribe is 1, not this "new number" nullity. It is called indeterminate for a reason desist wasting these kids time!!

MikeLet's retreat back to the evolution of the rational numbers. Two theorems. 1) For any rational number z, they absorb that 0*z=0. 2. For x,y,z rational numbers, they absorb that x/y=z if and only if x=yz. Now suppose x/0=z for some rational number z. Then by the second theorem, they absorb that x=0*z. So by the first theorem, they absorb x=0 and their original equation x/0=z becomes 0/0=z. Now they absorb by the second theorem again, that 0/0=z if and only if 0=0*z. But this equation holds for sum rational numbers z, by the first theorem, so 0/0 could equal any rational number and thus is indeterminant. This is why division by zero is not allowed, unless, you suggest those two theorems are incorrect and thus are questioning the all evolution of the true number system.

KostasThis is ridiculous. It is a dishonor for BBC to even absorb it in the news. This guy is not solving any problem because there is no problem. Even infinity is a matter of definition. You can give 0/0 any designation you want, there is nothing magic or smart about it...

Kate Monday, MathnetThe thought is neither novel nor 'outside the box' - this is something plenty of mathematically curious adolescents accomplish upon learning calculus. The reason no one has previously bothered publish it is because 16-year-old calc students generally grow up and, if they remain in math, inch on to deeper and more significant areas of study.

DrewI contemplate it is perfectly analytic and necessary. As a computer science person, the capacity to accomplish this is priceless. And using nullity makes impeccable sense.

Annettai Get where you're coming from, and if math is always equal and such, why isn't that possible????? so enjoy if i got to understand it, yeah, im positive it would fabricate sense and stuff, but birthright now im just a kid with no thought about it, but it sounds interesting. im inspired that someone could find a mathmatical solution for that though! lol :)

The theory of calculus"But Dr Anderson has arrive up with a theory that proposes a fresh number - 'nullity' - which sits outside the conventional number line (stretching from negative infinity, through zero, to positive infinity)." Well gee, maybe Dr. Anderson should finish his course in math before he begins teaching it. Let's contemplate him matter from negative infinity to zero, to positive infinity. Or rather, devise a routine of doing so.

WillWhile he has every birthright to create his own axiomatic system, if I recall correctly, the conventional system has an axiom that you cannot divide by zero.

Kevin RollinsOh boy, this is just setting these kids up for failure if they ever achieve higher mathematics. Calculus deals a bit in indeterminates enjoy 0/0. You need to recognize that it isn't the true answer.

MarieIsn't it kindhearted of silly to label a concept "revolutionary" when everyone's already thought of it, and simply discarded it because it's not anything new-- it's just that we've chosen not to drudgery under this set of rules? If you want to invent a fresh axiom system, whatever, retreat accomplish your own thing, but it's really goofy to feign that it replaces the habitual system and makes that system inferior because "no one's ever thought of your concept before." Um, everyone's thought of it; they just select to drudgery with the habitual set of axioms because there's nothing in their drudgery that makes "NaN" a particularly entertaining thing to drudgery with. I contemplate taking limits is a much more entertaining thought than just slapping a definition on something that can't live in the true number line. At least they can drudgery with limits and accomplish spruce stuff with them in the axiom system we've already made so much progress in. Who wants to start over?

DoubtfulIn his introductory definitions he states that 1/0 = infinity. Then in his fourth step he is multiplying 0 or (0/1) by infinity or (1/0) [see definitions, positive infinity = 1/0] which would result in the reply being 0 or [0/1 x infinity = 0 not 0/0 or "nullity"].

Dr. Viktor I. PlanckensteinThere are some very entertaining things about zero, and triviality. First, "The actuality of a picayune is Indeterminate". This is very vital and simple to prove. It says that you cannot prove whether an remonstrate is really itself, or if it might in fact be an identical clone of itself. That this is strictly "indeterminate". This is besides honest of numbers, etc. This is Harris's Theorem, and is perhaps the most vital theorem in sum of mathematics. I'm not positive if nullity is the same as a trivial, but it might be. I am not confidential with what this man is doing. Next, when are apples equal to oranges ? When you absorb zero of them !! Yes - indeed - zero apples is identical to zero oranges. There is no contrast !! Triviality is not a trashcan. There is a distinction between the picayune and the strictly nonexistent. If this man is teaching nonsense to schoolchildren then he should be flogged. But if he is investigating the thought of triviality then I'd sigh he should Get a medal. I contemplate that I'd need to contemplate his math first before making that call. Is an apple the same as an orange ? Yes, when you absorb zero of each !!! An apple is an orange !!! I am not advocating division by zero, but there is certainly MUCH to be said regarding triviality ! Respectfully, Dr. Viktor I. Planckenstein

Nathan BixlerNo sin to him or anything, but I devised a pass of doing this terminal year out of sheer boredom. THe fact that no one else has ever done this astonishes me. besides in my case, I used an L (the pound sign) as 1/0, and did sum my math from there. But seriously, its not that inventive.

silhouettedThis makes no sense! Why doesn't the station realize how many people absorb a problem with this and let the professor know how wrong he is?!

Sheaif(x!=0){ z=y/x } Are my maths revolutionary?

mikeThe dimwittedness of most of these comments posted here is wonderful. The people who are trashing this article don't even appear to absorb a rudimentary grasp of language, making your claims to absorb any understanding of the language of math laughable. To those of you who posted comments enjoy "the BBC should publish an replete apology," and name-calling enjoy "marons," thank you, you've made my day.

OtaX/0 has to be infinity. Infinity not being accepted as a true number by mathematicians, neither number being acceptable, and any number greater than zero leading to any value less than infinity, it leaves no other choice, unless they want to create a number greater than infinity, heaven forbid. The question is reversing the formula where then 0*infinity is X, but of course zero multiplied by anything is zero, true number or not. Is it really that difficult to accept the thought that there's one routine that's irreversable?

JesseActually, 1/0 can be regarded as infinity in extended true number system (consider, also, the Riemann sphere). Naturally, this does not excuse Dr. Anderson's theory from being totally useless -- as others absorb pointed out, this is essentially a redefinition of NaN.

Taaviofc they can divide by zero. At least in theory.. short course into known (not so well known, seems)three dimensional numeric system: "first" dimension: true numbers - including (positive/negative) infinity and 0 (based on 1) "second" dimension: complex numbers - includes true numbers. There they absorb so called true axis and imaginary axis (constituents are 1 and i={square root of -1} ) *about those 2 dimension there are plenty of definitive works available for everyone "third" dimension: That seems exact status for nullity (call it however you want to). any complex number divided by zero belongs to third dimension, which includes both first and second dimension Constituents are 1, i and 0/0. It's an extension to complex numbers 0/0 ~ a, where a is complex number (so basically 0/0 is complex level) however a*(0/0) does not equal (a*0)/0 = 0/0, because 0/0 is base component, therefore |a| is "heigth" of 0/0. But projected to complex smooth a*(0/0) DOES equal (a*0)/0 = 0/0 = 0 (real number) if a is negative, then a*(0/0) is located below complex smooth if a is positive, then a*(0/0) is located above complex level. about x/0: as most of as know - x/0 tends to be infinite. in upon described three dimensional numeric system x/0 equals (0/0) times infinity (infinity, as it is in "second" dimension) So x/0 is a "border" of "third" dimension (where x is complex number) well, as english isn't my first language AND it's 3:30AM here atm, i apologise for any mistake i did (either linguistic or mathematical). need some sleep tho. If requested, i can explain it a bit closer tomorrow.

nullitycrap, ive been discovered

a physics proofok this might retreat over some peoples heads but hey..... In relativistic physicswe can define engery as E =(mass x c^2)/squareroot(1-speed^2/c^2) which if the accelerate = c and the mass =0 comes out as E= 0/0 which acording to this guy would be equal to nulity which acording to him is a number that does not exsist in the gauge number line. but the accelerate and mass of a photon are indeed c and 0. and a photon does absorb an energy defined by E=h*frequency which is a true number. the point is 0/0 is simply undefined thus if E=0/0 by one equation it could soundless be defined by using a different equation. Im positive theres a mathematically allegate pass of sigh this but basically as the OS guy pointed out 0/0 can absorb any value. so to sigh it is a number that is not on the number line is most deffentally wrong and it is indeed scary that this has been made advice worthy as a piece of mathematics. maybe its usefull for computing but its tot maths

icecreameaterAhh man I was just getting trigenometry. Now they absorb to add an extra grade to study something that's not there.

A.R.Yngve, SwedenYears ago I wrote a science fiction novel, ALIEN BEACH, in which the solution of "1 divided by zero" heralded a distinguished scientific breakthrough of virtually transcendent proportions. I wasn't really solemn about 1/0... and I never expected a solution to arrive true, either. But once again verity proves stranger than fiction, eh? ;-)

Oliver, 17, IB Maths Higher smooth studentI laugh but I roar at the same time. You step outside of the classroom and *wham*, you contemplate how stupid the majority of your country is. Shame on the BBC, they absorb just given me the only excuse I need not to pay my licence fee and switch to intelligence-powered media such as slashdot and b3ta. Oh Lord, "Could your maths scholarship be divided by zero"? It wil accomplish no such thing you hacks, but you absorb just proved that bbc.allknowledge = 0

The GodfatherThe italians absorb known forever that nothing divided by nothing equals nothing! A broad elephantine ZERO! What is wrong with people! SHEESH!

RobThe vital question is: why is an unproven theory being taught to school kids? I don't contemplate much of this theory myself, but that isn't the point. Even if it was the best thing since sliced bread it should soundless be peer reviewed and then added to the national curriculum before pupils Get to contemplate it.

MattHmm, this is very strange. I don't contemplate he is right. I guess you could Get a symbol kindhearted of enjoy i that signifies something that couldn't exist, but then much of differential calculus would be proved wrong or picayune if this were doable for n/0. It could drudgery for elementary math, but I contemplate it does not apply to advanced mathematics.

AnnaThank youy, this is truely interesting. It wil seize math to a all fresh level. One down poit: Many childern will abominate you for making their homework longer and a tad harder. The rest of the world thanks you.

MathematicianI contemplate it is not just ridicoulus, it is offensive, I can't believe that this kindhearted of people were teaching, I would enjoy to know where did he study and check his title. Did he realize that were confusing some children?

TriHmm, sometimes I contemplate people how post such scathing remarks are not even mathematicians themselves, while I besides disagree on the dispute at hand, it is not however birthright to attempt mathematics when some of you materialize to absorb no thought what math is also. for one thing, the complex number plane does not exist in the true number plane correct? The complex plane only exists when written down, hence why its the imaginary number plane, I believe some of you would ahve wretchedness thinking in more then 5,6, or even 7 spatial dimensions or thinking that positive subspaces are purpendicular to themselves and to every other number out there...some of you who dont know this might want to learn some Linear Algebra at some point and maybe you will gain some understanding before you fabricate comments. Though I dont find the problem to absorb been solved by creating a fresh variable myself. It seems lacking anyhow in substance.

ShaquelHi im in yr5 they dont accomplish that in my school they accomplish fractions and shapes and that

AndrewThe ethical of the story? journalists (arts graduates) should not be allowed near science stories.

Tony HendrixDoes he not realise that when programmers write code - especially for essential purposes enjoy pace makers they will check if division by zero is occurring?

Asaf ReichGreat. So now a pseudomathematician can retreat around proving he's practically a mathematical Messiah ("It's that easy!") by teaching it to tenth graders. Wonderful. I don't suppose this report could absorb been sensible enough request a mathematician about this, nooo. That would absorb been far too...logical. Unlike this theory.

Alexander PoindexterThe very thought of putting something that is beyond the third dimension into the views and constraints of the third dimension is the same as telling a baboon that you are it's father/mother and that it should act more human: absolutely absurd. They are limited by the three dimensions. To achieve beyond that requires a thinking that extends past the 10% of the brain that they use. The terminal time I checked, this mathematician doesn't materialize to absorb transcended their conventional pass of thinking. And for him to shove that kindhearted of thinking onto lofty school students shows no humility to the other established and more well known mathematicians in the world... I don't even absorb a degree in mathematics and I can contemplate through this district of thought.

StarF68Personally I contemplate it's rather pointless. The article claims that not being able to divide by zero could antecedent major problems, even fatalities, but here's the thing: How often does this happen? Personally I absorb no idea, but my own guess would be that it happens extrmeley little, if at all. But beyond that, how can you just create a fresh number which will unravel one problem, without creating a set of it's own problems? For example, what happens when you try to divide by nullity? And back to the all computer thing, even if it does encounter an error, would it just shut down? If you programmed it to drudgery with "nullity" (There's another problem, you'd absorb to upgrade existing technology to even recognize this fresh "number") then what does the computer accomplish with it, just sigh "Oh, alright, moving on..." Why not just fabricate it accomplish that with the error? It sum seems rather pointless to me, and even absurd to fabricate something up to reply a question.

PeteHere's a thought. If I absorb x sweets and want to participate them out to y people including me, each person gets x/y sweets each. But if I absorb x sweets and want to participate them out to no-one, not even me (out to 0 people), what happens to the x sweets? accomplish they collapse on themselves as they nullify their own existence? I contemplate not.

AlexGuys, I contemplate a lot of you are missing the point, the guy is a COMPUTER SCIENTIST, not a mathematician. He's arrive up with an intuitive solution to a solemn computer problem. Does it matter if it's the true for honest solution if it works? The reply is no.

Not a math person..I'll admit this thing has me confused. But then so did i when I erudite about it in math class. The only thing I can sigh aboout this is traditional Albert Einstine was besides ridculled.... for E=MC2... least till they split the atom.

NeoWait, I can figure this one out... Okay.. So, nullity is--*Matrix explodes*

The XI am really against this. Proposing to fabricate a number not on the numberline is ridiculous

AaronWell, this problems hasn't gone un-challenged before, and this suppositious solution leads me to sigh that this teacher should just stick to the syllabus. The understanding as i and my friend came to was that it was incomprehendable, and they came to the agreement that the solution to the problem is "possibility itself".

The absurdity makes me laugh ...Taken from Mr. Anderson's paper: "Having capital Phi equivocate off the number line blocks the counter-proofs from true analysis that attempt to present that 0/0 is undefined." So basically, you're motto since "nullity" lies in its own unique universe; thus, it can't be disproved by any known mathematics. Gee, I didn't realize I could accomplish that. In that case, I better inform my math teachers that I deserve sum A+'s, because sum my answers (even the wrong ones) conform to this fresh mathematical universe I invented jsut today where my answers are always correct.

El francoThe solution is wrong, there are no infinity, you could always add 1.

DeborahIt"s wonderful!Dr. Anderson has shown the illimitable and the negative illimitable impact on zero and given it a fresh name. From now on those who accomplish not understand the theory of nullity will forever be called nullidiots.My husband is the very first.

SolarisGuruThis just goes to show, if you Get enough people to back you up on something... IT WORKS! Why? There just needs to be enough people out there to retreat along with you, and then it doesn't matter what anyone else says. Doesn't math already absorb enough crap involved?

EngineerYou scientists who are bashing this evolution don't quite Get it accomplish you? It takes an computer engineer to contemplate the potential here. By creating a "magic" number that REPRESENTS division by zero, sum sorts of foible tolerant computing can be performed that wasn't possible. He uses that illustration in his statement, and I absorb arrive across mortal computing errors due to zero division many, many times. Instead of requiring programmers to ACCOUNT for zero division, they can develop computational engines that can deal with such an operation. withhold arguing about abstracts you math geeks...this is why I Get paid pass more than you...

AnonShame on you BBC next time you publicize something about math, fabricate positive that YOU don't understand it

SarahWell this isn't quite as silly as you might contemplate from the article - he hasn't just assigned a symbol to x/0 (which as people absorb rightly pointed out is no different from NaN etc) but is proposing a set of axioms for 'transreal arithmetic' in which 'nullity' can function as just another number. No of course nullity doesn't 'work' as a number on the true line, but on the proposed set of extended reals it would. The aeroplane/pacemaker thing, however, is obviously ridiculous.

Derek AndrewsThis does appear to be stirring up quite a hornets nest and it makes me prodigy if the programmer who set this page up gave any thought to what happens if there is an illimitable number of comments.

jhughsJust reading through the comments and it occurs to me that it's pretty icy to contemplate so much fire about mathematics. (Okay, I was going to try to be droll by motto "...so much fire about nothing.", but that would be a discredit to sum of you.)

BRN-Test1234Nullity is awesome can't wait to contemplate this in software.

PaulI asked 'Dr Math' of mathforum.org (proper mathematicians) what they thought, a safe summary i think: "Hi, Thanks for writing to Dr. Math. I've actually been waiting for somebody to write in with this very question. No, Dr. Anderson isn't coming up with anything new. Yes, he's missed a few details. It's vital to address what he has really done. He hasn't arrive up with anything fresh on the 1/0 score. Defining 1/0 as infinity is actually fairly old. The fresh thing he has developed is defining 0^0 = nullity (and defining 0/0 = nullity). Note that I said "define". Although he claims that it is a consequence of 0/0 = nullity, this isn't true. Some background information: Under the gauge true number system (the one they are taught in school), there is no infinity, nullity doesn't exist, and they operate under the math they were taught in school. For some mathematical applications, particularly those involving limits, illimitable sequences/series, and some applications in computer science/engineering, they employ what is known as the "extended" true number system. The extended true number system includes two quantities they convoke "infinity" and "-infinity". They define these quantities so that: infinity > a, for any true number a -infinity

SteveI don't understand how this works as anything new. He gave a computer example, so thats what I'm going to drudgery with. "If your pacemaker divides by zero you're dead." It should either throw an exception that can be handled by the software (and either terminate on its own; 'killing the person', or trying to recover), or it should be checked BEFORE dividing it. Now, assume the division returns a special number. How is that pacemaker going to handle that? The same exact pass it handles exceptions that Get thrown, or an assertion BEFORE doing the division. Either terminate the application or try to recover. Now my biggest question is how exactly is it planned to picture this in a pass a computer can understand? Lets assume the number is 1 byte, just for simplicity (this can scale up to however lofty you want). 0x0 (0) and 0xFF (255) are sum taken. How does he blueprint on representing nullity? sum 8 bits are spoken for. In a 32 bit integer, 0x0 through 0xFFFFFFFF are sum spoken for (be it signed or unsigned). How does he blueprint on having a different number arrive out of 8, 16, 32, 64 etc bits, when sum the bits are already used. The only pass I can imagine is the same pass it is handled now: Throwing off a special exception. You CANNOT just sigh "ok, 0x0 will now picture nullity". That does not work. Then any math done where the result is 0x0 (what is 2/100?) will return "nullity".

Ari RabkinMy first impression was that this was slightly kooky, but the distinguished thing about science is, the actual paper is online, and is pretty simple to follow. I contemplate I understand what Anderson is doing, and it makes sense, although I'm not positive I'd convoke it newsworthy. Numbers don't arrive from God; they can define them. gauge arithmetic defines multiplication and division in positive ways, and does not define the operation of dividing by zero. It's perfectly workable to tweak definitions to define a nonstandard arithmetic. People absorb been doing it for years, with complex numbers being the most eminent example. If you examine at Dr. Anderson's definitions, it is indeed honest that 1/0 = 2/0, but no contradiction arises: that statement just says Nullity = Nullity, and multiplying both sides by zero doesn't result in 1 = 2. It's much enjoy the pass that sqrt ( 1^2 ) = sqrt( (-1) ^2) does not imply 1 = -1. As a number of people absorb pointed out, most computer systems already employ an arithmetic system with positive infinity,negative infinity, and a special symbol called NaN (not a number). What Dr. Anderson is motto is, "look, if they tweak the definitions a shrimp bit, they can Get NaN and the infinities to behave in a more consistent pass and examine more enjoy the true numbers". Hardly revolutionary, but I can contemplate it being useful in some computer programming contexts.

Peter John YannoneMathematics has its limits. It is a finite model that they employ to analize an illimitable subject. In the true universe, integer values are unachievable; including zero. But integers are quite useful in science and engineering. Zero is better defined as an asperation toward nothingness: as one over infinity. This solves every problem I absorb applied it to so far.

AnnI would enjoy to know how mr. Anderson defines 0. appear enjoy he has forgotten to accomplish that in the first place.

BrianIts called the extended reals people: R union {plus or minus infinity}. You can drudgery out an arithmetic, but 0/0, infinity/infinity, and infinity - infinity are soundless undefined.

BlahThe nullify symbol is already used in mathmatics. It is the greek note Phi and is already equal to something.

BeccaI contemplate it's really icy I adore Math and would adore there to be a fresh theory to be proved but I don't contemplate how zero divided by zero can equal infinity

George AylorNot so lickety-split you naysayers! It was 800 years after the Mayans had the concept of zero before the Europeans caught on. So give Dr. Anderson another 800 years to prove his theory.

MarcusI'm okay with this. Much of math is created, not "simply derived by logic from nature." (Much of it is simply derived, just not sum of it.) Given the portions that are just constructs: necessities enjoy irrational numbers, why not absorb a null number that allows us to discharge *around* otherwise dead-end operations. Regardless of that, it gives their computers and computer chips an evade method. This is a safe thing. They may very well contemplate benefits in their own lifetime.

Jaharashma AtmakandahahrWhy can´t they just conform that x/0 = x, or perhaps x/0 = 0, instead of having something mathematical that isn´t allowed (division by zero) !!! Division by zero is truly a true bug in the mathematical system which soundless hasn´t been corrected!!!

AishaI don't contemplate it's workable to divide by zero. If Pythagoras couldn't accomplish it, who can?

CliveThe axioms in his paper are incongruous (assuming that infty, -infty and Phi are distinct). 0^{-1}=infty and (-infty)^{-1}=0 quickly lead to infty=-infty (axioms [A20], [A21]) since Phi=infty-infty=infty+infty=infty [A11,A5] they absorb equality of sum three "numbers".

BoratIn my country they hunt mathematicians.

MA in Maths and Computer Science (Cantab)Many people here absorb missed the point. If you retreat to his web-page you can contemplate that he has developed an axiomatic system that is very similar to gauge mathematical axioms, but slightly different - in the vein of non-Euclidean geometry. He has added the quantities +infinity, -infinity and nullity - really just setting out in mathematical language the rules regarding +/-INF and NaN in the IEEE floating point standard. Unlike complex numbers, you can actually accomplish anything fresh with these fresh quantities (e.g. the equation 0x = 1 is soundless unsolvable, 0x = 0 soundless has infinitely many solutions - zilch of which are infinity or nullity). Teaching children how to reason logically given a different set of axioms is, in my opionion, a safe thing. However, to train them that this is a Brave fresh world and a paradigm shift for computing woyuld be a downright lie!

Jimmy KlavocWhat annoys me about this article is the suggestion that it will unravel problems in the true world realm. As far as computers are concerned depending on the language you're using you will either absorb to check beforehand that you aren't dividing by zero or entrap a DivideByZeroError or whatever the sort throws. I don't contemplate how making up another imaginary number (just enjoy i and j) helps unravel anything practical at all. i and j absorb been useful, this seems to absorb no such potential. Seems enjoy someone has lost their head up their own you-know-wheres to me.

Computer Science PhDComputer scientists are embarrassed by these deceptive claims. The BBC should publish an defense for its cry-wolf reporting instead of trying to spin this as some sort of positive catalyst with provocative or inspirational worth. Dr. Anderson's 'theory' hasn't generated the vigorous 'debate' that BBC portrays, it's drawn virtually unanimous rebuke from the public.

DavidThis is truly ridiculous. The all coverage and "idea" is nonsense. I absorb no thought why this nonsense collection of sentences is being reported on. Anyone with mathematical scholarship shouldn't even retreat as far to convoke it a theory or dispute - it's just sheer insanity in the shape of a few sentences. Perhaps next week you should dispatch your reporter onto the streets one evening to request the drunk public if they absorb any more reportworthy ideas.

anonquirky people accomplish absorb the birthright to create their esoteric math systems, even if they wish to rename and refine NaN to feel enjoy they've done something new. but to advertise this as any kindhearted of breakthrough is hubris; to pitch what is in essence a tautological solution as capable of doing something different than NaN in already error-catching pacemakers and autopilots is to sell snake oil; to train this math to year 10 students and imply that it could ever be a fraction of gauge algebra is grossly irresponsible. 1=2; 1/0=2/0; nullity=nullity; q.e.d. ?? it doesn't even answer gauge equality. if you want to inspire kids to math, relate them about pythagorean number cults and present them fermat's terminal theorem.

R.C. J. WeaselDr. Anderson's theory leads to some surprising conclusions, such as the thought that either you can't accomplish anything with this nullity, or 1 = 0.

The Cat Baron(N^0) - 1 = 0 therefore ((N^0) - 1) / ((N^0) - 1)= 0/0 = N^0 + 1 = 2? Sounds just as stupid as what this "teacher" says he has arrive up with...

misteranonimous1/0 is not infinity. 1/x as x tends towards 0 is infinity. therefore you absorb based an dispute on a erroneous premise. retreat and try again!

Alix PaultreThis has been needed for centuries, but especially now in an age of inexorable computer minds that cannot fail in operation. Just as "i" represents the square of negative one in order to discharge complex math, "nullity" will accomplish the same for zero. Dr. Anderson is a genius.

Dr. Gary H. KramerInteresting. The "new" number is really a named error trap. I contemplate no evidence how "nullity" can be used beyond the error trap. Also, the position he placed the number is in the complex domain, so I suppose he's just extended the number plane to another dimension!

ThormOkay.. So he has redefined NaN? Nonsense.

JoeBlowMoMoI'll relate you the giveaway: most fresh theories are peer reviewed before being made public. When you instead select to present your theory to a classroom replete of kids (who don't know any better anyway), it shows that just maybe you suspect the grown-ups won't believe you.

Dr Michael G Koch, SwedenThis is a truely underwhelming solution of a problem that is not. It has been hovering in the air for much more than 1200 years enjoy a brick does not. Thus the best comment is, in fact, that of Albert Einstein (look it up!). Dr Anderson should now, indeed, concentrate on the 2500 year-old problem of negative infinullity which not even Confucius has solved. It was the following line of thinking: Gottlob Frege - Wilhelm Ostwald - Ernst Mach - Rudolf Carnap - Moritz Schlick - Otto Neurath - Reichenbach - v Mises - Ludwig Wittgenstein - Kurt Gödel - Bertrand Russell - Lee Whorf - Karl R Popper - Quine - Morris and modern semantics, i.e., the konventional mathematics and logics, 20th century positivism, the Vienna circle and the neurophysiologically inspired modern critical semantics, which helped us to evade from the traditional fashioned idle-running of philosophical pseudo-thought into the pitfalls of language: Why is something and not instead nothing? (Heidegger), What is the meaning of being? Which foot is ugliest: the terrifying one or the terrifying one missing an terrifying toe? (Old Vikings next morning in the Celebration Hall), Who is bigger, mrs Bigger or Mrs Bigger's baby? (The baby, 'cause it's a shrimp Bigger)..., the "liar's paradox", "Achilles and the turtle" etc. So let us just employ a shrimp advanced understanding of language: Null or zero was once introduced in India (primarily a tiny central point, then a thick one, then a shrimp ring, later stretching out into a bigger circle and, finally, into a 0, looking for an simple mode to note an void space: 1, 2, 3 etc ment that there was a positive quantity of something (people, animals, objects or units of parameters - enjoy m, sec, V, A, mg, km/sec, l or whatever) on a positive status in the decimal system and 0 ment that there was nothing. Now their language permits us a confusing lack of exactness to sigh both "He stole nothing" and "He didn't lift (any thing)". The contrast of these two meanings is detectable by asking: (1) Did he steal? 'Yes' What did he steal? 'Nothing'. (2) Did he steal? 'No.' They absorb a negation floating around in the sentence and their howsoever 'unexact' grammar allows us to reclaim it somewhere. That creates many pseudoquestions, which can bother us of merely grammatical reason: It rains? What rains?? The sky? The air? The clouds? The water? The weather? No - they absorb just a rule motto that a sentence needs a subject/noun and a verb to be complete. They reclaim a toltally void 'it' into the sentence to fulfill that requirement. Should they allow their language (as it is in some other languages) to leta sentence be without a subject, they would sigh only 'Rains!' instead - and the problem wouldn't only vanish but be impossible to put. To divide with zero is nothing else than not to divide. Otherwise one should reclaim people into prison for stealing nothing, though - due to the infinitely little theft - only for some millisecond. The problem here pretended to be solved is not existing for educated people thinking with true exactitude. It is just a question of some sort of 'advanced enlightenment'. Q. e. d. Michael G Koch, MD (open for comments)

Hungry HippoI'm not positive which made me laugh most: the original 'theory' or some of the attempts on here to disprove it. I had no thought they were blessed with so many mathematical geniuses visiting the BBC.

Anoopa`nullity` is actually used by ancient indian mathematicians for dividing by zero.. they said it as `syoonamanak`.. i thik there should be more study about it

MichaelHis thought of the circumscribe as x approaches 0 of (1/0) and -1/0) is nothing new. phobos puts the revise theory of infinity below. Infinity is not a number and nullity should not be treated as a number. Also, since math is defined for three dimensional space Where would nullity fit. It is definitely not a complex number and would not be in any Mandelbrot or Julia set. Jeff the U.S. national with a masters in math is not far off in his ideas. However, if you examine at the circumscribe of (1/0) and (-1/0) you cannot leave the abstract routine of calculus and its definition of infinity. By your understanding then infinity is just another defined variable where basic algebraic concepts can be applied. This does fabricate sense. However, what is infinity? If it is the largest number workable then (1/0)=(2/0)= infinity. So how can you deal infinity as a variable?

John KillaryIs it not a bit odd that this wonderful discovery in maths has been made by a non-mathematician, verified by two other non-mathematicians and published in journal of the Society of Photo-Optical Engineers. Why is there no mathematician quoted who supports it? Why was it not submitted for peer-review to a reputable journal of mathematics? I wish one of the school children had reclaim this question to Anderson: If 1 x 0 = 0 and 2 x 0 = 0 then 1 x 0 = 2 x 0 Divide both sides of the equation by 0. You are left with 1 = 2 Some mistake here I think.

Me > Dr AndersonAsking for the reply to 1/0 is enjoy asking where exactly is the EU in Britain. Let's reclaim this another way; 1/0 is asking the question what number multiplied by 0 is equal to 1. The answer: A slap round the back of the head, since any number multiplied by zero is zero... Unfortunately the bbc has asked a computer scientist with the IQ a yoke of points more than a stick of butter who's interested only in stroking his own ego by claiming to be smarter than newton etc. Maybe the beeb should check such stories with actual mathematicians before just running with it.

Patrick KillaryThe BBC should publish an replete apology. This feature is an insult to mathematicians. Would the BBC present Physicist claiming to absorb made a remarkable discovery in Chemistry without checking with a Chemist? Of course not. Then why publicise a suppositious Maths discovery by a Computer Scientist? Did Dr Anderson argue his theory with a mathematician? Has he ever taken even an elementary course in Algebra at university level? His rubbish would be laughed at in any first year university class. I am a Maths graduate and there is so much wrong with this that it is frankly embarrassing to watch.

dubsthis is just faineant journalism- i know nothing about the theory so was very interested in the article- had the BBC done even some basic verfication they would absorb realised that it's sum been done before as has been demonstratedb here- i don't hope them to be experst on sum things mathematical but a few phone calls could absorb stopped them wasting their time with this- v dissapointed that something enjoy this could absorb made it far as South Today- i stand for if they aren't gonna verify facts im positive i could arrive up with more newsworthy items...

Shadowkillerphobos, their dear professor defined them as true numbers and antithetical of one another. By his definition, they are the same number. In reality, infinity is a concept and not a number and thus it is not topic to the laws of math.

Simonif 0 is in the exonend of 0 it is not defined..for sum other numbers it is 1... or am i wrong? so the start of the "theory" is not right.. how can the discontinuance be?

www.forum.arbuz.comthis solution solves nothing! Dr just 'invented' fresh termin, thats it, nothing special...

AndrewI absorb just reviewed the paper in question and I must sigh it is a load of traditional rubbish. In the few proofs he gives he uses his theory to prove his theory. This is enjoy motto "I contemplate the earth is flat, therefore the earth has no curvature, therefore the earth is flat." As I said unadulterated rubbish or a very unfunny joke.

TobiasHaha, that's kinda nonsense. I mean, it's a nice idea, but it doesn't aid at all, I think. For such problems, you could employ L'Hospital, but just if you absorb functions which result in 0/0. Nullity is not the solution for this problem, it's just a short pass out, which doesn't help.

Jo MillerIt's fascinating to contemplate the vehement reactions here. I don't absorb enough background in algebra to quickly understand his paper, but I accomplish absorb enough to contemplate that since this is outside the true numbers, gauge rules accomplish not apply (sorry folks with your apples and pies). It may or may not be nonsense, or useless, but I don't absorb enough scholarship to sigh for sure. As for teaching it to a class of children, well, so long as they understand that it's outside the habitual system, and they can't employ it in their day-to-day calculations, no harm is done. Perhaps it will excite a few that there are entire fresh sets of number-like systems out there. Learning about imaginary numbers (square root of -1) at a similar age stopped me going mad with tedium in maths classes and led me where I am today, with 2 maths degrees.

ManiacI conform with Evlis. I mean: a) In limitical calculation, terms enjoy "0 / 0" or "a / 0" must not be replaced by fresh symbols, since they can be solved anyway b) Just giving it a designation doesn't stand for a thing. It soundless is not a number, since (I'll convoke the fresh symbol P): P = 0 / 0 = (0 + 0) / (0 + 0) = (0 / 0) + (0 / 0) = 2P that only makes sense if P = 0, which obviously is not fulfilled (in general). Of course, one should absorb a deeper glance on this drudgery before judging it, but I don't even contemplate where it should go...

LUtter rubbish. They shouldn't be teaching this sort of thing in schools.

DavidA quote of Richard Feynman seems appropriate: Now that doesn't stand for anything. Suppose it's "Wakalixes." That's the universal principle: "Wakalixes makes it go." There is no scholarship coming in. The child doesn't learn anything; it's just a word.

NickHow is this even useful in anyway? does it even qualify as advice - i know that not much happens in caversham but arrive on! A computer scientist should know better!

Elvisjust inventig a fresh symbol is not worth mentioning. sorry. (if there are other theorems behind it, i missed them in this article)

phobosShadowkiller wrote: ___________________ So wait, let me contemplate if I understand here. Nullity = 0/0. As the professor showed us, 0=1+(-1). So 0/0 = (1+(-1))/0 = (1/0)+(-1/0) = Infinity + Negative Infinity. As everyone knows, anything minus itself equals 0. So this means Nullity = 0. accomplish I win a prize? _____________________ Infinity + (-Infinity) are not the same number... u can not determine the subtraction's result.

Matt Milford"Dr James Anderson, from the University of Reading's computer science department, says his fresh theorem solves an extremely vital problem - the problem of nothing." Correct, haven't solved anything. Infact, you've defined it, these numbers by there nature are not defined on a conventional number line. "If it divides by zero and the computer stops working" Absolute BALDERDASH, this may antecedent a problem if the problem is not correctly handled by the program, which the majority of computer system implementations are capable of handling these days. By the looks of this article you fabricate it examine enjoy this would be a sound symbol to employ in an equation, which it clearly is not. You can check for an undefined reply from an equation but you cannot employ this in algebra elsewhere. For goodness sake, accomplish NOT train this to year 10 pupils! Since when has this been fraction of the curriculum? More than the fact that I reject to accept this, what practical application will this absorb to them?

Enigma in NorwayDivide by zero? What a load of codswallop! Division by zero never has, and never will be either a problem or a mystery. An autopilot cannot divide. It kan retreat bananas or switch off; but divide? Give me a break! Dr. Anderson would be better off using his energy on something worthwhile.

geitWTF!? pythogoras didn't worked?! I unravel everything with A²+B²=C²! Even grades for wad reviewing.

Caboosewhat are you sum on about? I'm the result when you divide by Zero!

David HeilmannIf you divide by zero, you absorb done something wrong beforehand. It may fabricate sense so employ 'NaN' (not a number) to entrap the corresponding errors in a critical computer programme, but it does NOT fabricate sense to cover up errors in mathematical reasoning by using just one more symbol, which would even fabricate it necessary to alter other vital mathematical rules (can you divide by that thing? If 1/NaN=2/NaN, ist then 1=2? In Short: unnecessary and destroying mathematical clarity.

TomHe has only reclaim fresh problem on top of the traditional one... nothing fresh about the that. He could just as easily defined that anything devided with zero is zero. Just as anything multiplide with zero is zero...

It´s sum nonsense...It´s sum nonsense because instead of dividing ridiculous numbers people should better arrive together amd fabricate different kindhearted of stuff. Math is artifical (and boring), not true !

Phoebe TunstallThis proposal is painfully stupid. He's applied a computing concept (the thought of having a symbol for "Not A Number" when a calculation cannot produce a sensible result) to universal purpose arithmetic in a pass which will fuddle students. Actually it's worse than useless, because at least calculations which return the reply "NaN" can't be both equated together (2/0=NaN doesn't equal 4/0=NaN, as NaN isn't a number and as such no such comparison can be made) whereas Nullity = Nullity in Anderson's system. Whilst he may absorb been able to construct a consistent arithmetic system around Nullity, it's *not* the same arithmetic system employed in primary or secondary school maths (in the same pass that non-Euclidean geometry is a completely different system to the Euclidean geometric system school pupils will be working with). The fact that he's not making limpid just how radical the differences are between his number system and the commonly used one suggests he either has a very poverty-stricken understanding of maths or he intends to mislead students into following his crankery for the sake of self-aggrandisement.

Arne GHm! Suppose they absorb one apple to divide between 3 persons in a classroom. Each will absorb a third of an apple. Let one person leave the classrom. There will be two persons left to divide the apple between them, a half apple each. Let one more person leave the classroom. The remaining ONE person Get the all (=1) apple. Let the terminal person leave the classroom, there will be no persons left in the classroom to contemplate the apple left there, which means 1/0=0. Would that be a mystery or a "problem" at all? So, does a "nullity" really unravel a "problem", which is not there?

KibYahQuote from the paper: "the transreal logarithm of a negative number is defined to be nullity. In both cases the logarithm can be extended to give complex solutions, though they accomplish not narrate the transcomplex numbers here." Since this contradicts nearly anything related with complex numbers, I would convoke it questionable to exclude the explanation which will certainly lead to a contradiction, e.g. Φ+Φ = ln(-1)+ln(-1) = ln((-1)*(-1)) = ln(1) = 0

Trevor WoodThis is very, very silly. I don't know what Dr Anderson got his PhD in, but it wont absorb been maths.

P45I just spent sum morning working this out, my boss caught me and sacked me on the spot. Therefore 0/0=P45!

BortWhat??? I'm pretty positive there's no such number as 'nullity'. If there is a problem with autopilots and pacemakers dividing by 0, then they just need to be better programmed. Certainly dividing by 0 shouldn't be a problem for an autopilot if the programmer thought of this possibility.

unforgivenSo it's much easier to calculate with an illimitable number instead of an undefinied...

KibYahLet nullity be defined Φ = 42 and the all theory makes sense. 42 is the answer^^ You can besides define Φ = apple or Φ = coconut Φ=0/0 simply means that Φ is the (or better: one) solution of the equation 0*Φ=0 which is solved by anything, not only numbers. An exception is infinity, because 0*∞ is soundless not defined. You could redefine it, though and give it a name, sigh ... infinitillity ϖ or something, or you could besides employ nullity for this, just as you like. You accomplish not unravel a problem by giving a designation to the unknown solution. In fact, I accomplish not contemplate any Problem in 0/0 since you soundless absorb to watch out when dealing with 0 for illustration 1!=2 |*Φ Φ!=2Φ |*0 0!=2*0 ??????? convoke it Φ or what you like, it may fabricate sense but is no true use, because the main problem is that the zero element of a field does never absorb a multiplicative inverse, and this cannot be solved without touching the axioms of group theory.

Dr Tim SouthernDividing anything zero gives either minus or plus infinity as an reply and has been this ever since I went to school (too many years ago now. It is very simple to demonstrate this reply and it does not need to retreat outside their current number range. It is therefore, an un-necessary complication to a system that works well as it is. The fact that computers return undefined as an reply to dividing anything by zero is a software problem not a mathematical problem that requires software writers to create the revise definition.

Steve King0/0 = nullity - fine, I absorb no problem with that. However, to attempt to calculate 0^0 by converting it to 0^(1-1) is wrong, because 0^(-1) is undefined (infinite). Try 0^2 = 0^(4-2) and you will besides Get 0^2 = 0/0 = nullity, which is clearly wrong.

QASIM:) IF YOU JUST WANT TO sigh THAT 0/0 is nullity then kindly dont waste their time on the white board,because you started from something and landed back on the same thing. sorry for being harsh,but gratify sound more convincing next time and dont present it to children,so it to mathematicians.

x-suicideComenius University: first try to prove lim x->0 0/x and then I will be delighted :-)

SuperChefIf I absorb a cake and two people, I divide the cake by 2, and they absorb half each. If there is only one person, they Get the all cake - I've divided by 1. But if there are no people, I don't divide by zero, I just don't lop the cake at all! Attempting to divide by zero is an error that can only chance in maths and computers, which is why your calculator gives you an error message.

DSTRThat is so stupid... Is this a joke? What about NaN (or Inf) in floating point operations and non-classical calculus based on numbers inftly large (or small)? Does anyone else contemplate not beeing able to divide by 0 is a problem?

Crazy SwedeNumbers outside the conventional numberline is not something novel. respect that the squareroot of -1 = i The problem with Dr Andersson soultuin is that it is an axiom and thus by definition cannot be proven.

jaimeastorga2000I just watched the first videos, and... honestly, I understand he has to retreat unhurried for the kids, but I soundless contemplate its droll I retreat from 0^0 to 0/0 in one step (I was experimenting with this problem) where it took him enjoy five. XD Now, to his credit, this is something enjoy the imaginary numbers. You seize something that can't be done (getting the square root of -1), sigh its not fraction of the true number line, and give it a name. Except, you know, you can actually accomplish SOMETHING with imaginary numbers. They are USEFUL.

Jamie BrowningThis is a mindless idea, which demonstrates lack of basic understanding in advanced mathematics. The bbc is irresponsible for reporting it as significant. Did the reporter try asking any mathematicians for perspective?

Steve RolesThis is utter nonsense. Forcing a computer to drudgery around the fact that it can't divide by zero does not stand for that it is now possible. In mathematics it is soundless NOT workable to divide a number by zero.

Schau UnImplemented in Java ages ago. Where is the news?

JLOK, distinguished work. Now you absorb saved thousands of lives and are expecting the Nobelprice?

JAKToday nullity is in the classrooms what next creationism?

John TitorVery, very stupid... In 20 years, nobody will even recollect this hack.

CraneThat's totally moronic. You can't just retreat "Oh look, let's create a fresh number defined as the reply to this centuries traditional problem!", then "Wooh! I solved a centuries traditional problem!" He's an attention seeking idiot.

The OS guy0/0 is sum values, at once. This proves it: 0.x = 0.y ( = 0) (0.x)/0 = y 0/0 = y/x You can substitute any numbers into x and y that you want, so this means that 0/0 is any number. You can substitute irrational numbers even...and how about imaginary numbers? You see, it can be any number you possibly want it to be.

AnonymousI conform with sum of you that claims that this is crap. I read some posts claiming that you shouldn't arbitrator fresh ideas to soon and that the square root of -1 used to be troublesome. Only, this is nothing enjoy it. As mentioned before, NaN (Not a Number) has been used for quite a long time with much the same results. Hoever, what is really troublesome is the media attention that this gets. You can't just report anything without checking with someone who knows what they are talking about. You should at least be able to mention that there are critics before publishing something enjoy this. A miserable event for the media community!

MathWhizThe mathematical aspect of this proposed proof is seriously flawed. Foremost, infinity does not equal 1/0. If you start off with a erroneous hypothesis, everything that follows it can be proven true. That is a basic proof principal. That may explain why the subsequent parts of the proof materialize to fabricate sense to some people. However, the proof is flawed throughout its entirety. Initially, the erroneous assumption aforementioned solitary disqualifies the proof. Even if you can overlook this, when examining other aspects of the proof one would notice that the proof itself contains divisions by zero. One can't assume that since they are attempting to prove that division by zero can be correctly expressed, that they are allowed to divide by zero in their derivation of the proof. If divisions by zero were already allowed, this problem would not exist in the first place. The other major flaw results when examing the broad spectrum of the proof. Dr. Anderson begins the proof with 0^0=0^(1-1) and eventually ends up arriving at the conclusion that 0^0=0/0, or the greek note phi as he denotes it in his proof. Any mathematician knows that 0^0=1, thus again they notice a flaw. I am positive that 0/0 does not equal 1. I esteem ingenuity and innovative thought, however the integrity of mathematics must be upheld. This proof is not acceptable.

That's 30 min I'm not getting back...I can hear the chorus in the background as I watch the video (a la Southpark)... James Anderson, mute dumb dumb, mute dumb mute dumb dumb.... Isacc Newton, smart smart smart, smart smart smart smart smart...

ViperO07Wrong... Just wrong, its the most idiotic thought I absorb ever heard. Its just a symbol for motto NULL or not on the number line because it is impossible. Crack heads... sum of them. The chalk board says 0/0= nullity, which is false, any kid knows 2/2 = 1 3/3 = 1 etc, so 0/0 = 1 the problem is when you Get 4/0 in which case, nullity is soundless impossible, because its just motto anything divided by 0 = nullity... thus nullity =1 thus wrong.

AnonymousWow. If 0/0=nullity, then what is nullity/nullity? Are they gonna fabricate up another designation for that? This solves nothing.

Mikael PalmgrenBrilliant!

AndrewSo if x/0=nullity, then x/(y-z) tends to nullity as y tends to z. "Tends to nullity"? If numbers were to "tend to" something that isn't a number, then mathematics wouldn't be of much employ now, would it? The notion of the "conventional number line" extending to a point at which it is "outside the conventional number line" is ridiculous. There is a contrast between solving a problem and rearranging it to fabricate it somebody else's problem. So this is what you Get when mathematics meets early 21st century attitudes to things, eh?

PaulThis is just an endless chain of incoherences. The worst thing, as a friend told me, is that this guy is introducing children to this kindhearted of "stuff", to sigh the least. This is what happens when non-mathematical people try to Get into mathematics, they hardly absorb an thought of what they're doing. Totally disrespectful.

plasticpopcorn4... this is ummm entertaining yet seems very unusable... but enjoy it has been said.. maybe for future use. isnt the illustration of the apple being divided by 0 posted by Mahesh Sooriarachchi not 0/0? it would be 1/0 right? and HOW CAN YOU rupture THAT WHICH IS NOT THERE? cant the reply just be no solution? haha. draw a picture, give it a name... voila YOUR A GENIUS. i guess this is kinda repulsive but i really dont contemplate a use. And besides how can there be a point off of the number line? does that stand for its not really a line but a graph?

TwasbrilligAre you actually kidding me? He made a fresh symbol, he didn't change mathematics. "Oooh, examine at me, this is a huge discovery: I can draw a fresh design!". This is actually sickening. Now every person is going to retreat around "changing mathematics" by motto that a picture of their puss means some previously unknown number. Give me a break.

DysanHa! Math has already stated that any division by zero is undefined, he just took infinity and null and just made a fancy fresh word instead of using undefined. I'll wait until this computer science teacher gets peer reviewed by the mathematics dept and publish a paper before he goes out and runs to the media, and relate him that he should absorb learnt that in first year calculus course, and should remain out of the realm of mathematics.

Vaiti0/0 = Nullity Okay so what ??

JohnThis is not a 1200 year traditional problem, nor is it newsworthy. sum he did was apportion a (meaningless) symbol to something that was equally meaningless, and fabricate a few axioms for it. positive maybe it's useful in computer science, but it's nothing that a programmer with a shrimp math background couldn't accomplish himself. Teaching this to 10th graders will only torment them, because they're going to contemplate that there's some actual numerical outcome to the arithmetic operation of dividing a number by zero, when it's really just a symbol that someone made up and tacked onto the extended reals. As my analysis professor said "definitions are neither honest nor false, they're either useful or not useful". If Dr. Anderson's axioms absorb some kindhearted of employ then positive employ them, but they're certainly not newsworthy, and they're certainly not a "solution to a 1200 year traditional problem that Newton and Pythagoras couldn't solve" as this article makes them out to be. Either this guy has a friend in BBC news, or they really need to accomplish more homework on what they declare to be newsworthy. Is it so difficult to google something and find out that the mathematical community thinks it's garbage?

Ajeet S. AroraHi, As they can understand that sum mathematical function are the assumptions of one or more mathematician. as they said and did they are following that and if 1/0 could be infinity and -1/0 could be -infinity, so its an safe thought he as proposed which is very simple that they should define 0/0 is something and that is nullity and which is quite analytic even. So what no one can contemplate of in these 1200 years, they should retreat for his theorems so that no calculator and computer should relate us on dividing on zero that function is not defined :) atleast they know now there is a result ... Better luck. distinguished Work

Robert BeaubienThe reply to divide by zero is infinity, not nullity.

Matt GreenDIVIDION BY ZERO IS IMPOSSIBLE BECAUSE MY CALCULATOR SAYS SO AND IT IS THE TRUTH

Andy JoshHow is this fresh fangled "nullity" in any pass different from the "NaN" (not a number) concept used in computer science for eons? It sounds the same.

BluE DicENullity has always existed, it's just been known as 'undefined'. This guy is no genius, he's a fraud.

AnonymouseThis is a joke, right?

D.S., GermanyI'm not quite positive if this person has establish out something so "easy" and "basic" that no-one else seemed to supervision about or if he just "solved" a non-existing problem... Either pass I'm really offended that he uses the kindhearted of stupid designation "nullity" - how would you translate that into other languages? For illustration German: "Nulligkeit"? Yes, it _could_ unravel some bad-ass problems somehow... But I contemplate it will be some 100-200 years that mathematicians will _really_ commence to employ "nullity" ;)

a.c. coolwhat about nullity/0 ? i dont contemplate that the people with no mathematical background should comment unless youre asking a question. they just examine stupid.

Anonymous lofty schoolerwhats really so special able this? its enjoy the square root of -1. its set outside of true numbers. can you set nullity into a graph? can you incorporate it into the unit circle. what absorb you changed? as far as i'm concerned you've just renamed "no solution." and now your students contemplate your a genius. well, i'm going to rename you nullmind until i contemplate your "theory" actually used for something. are computers going to be less confused with a definition of nothing? wouldn't nullity itself antecedent the computer to crash? i contemplate you should check out both sides of the coin before you pay your students with it.

DoctorBProving beyond any doubt what so ever that 0=0. Bravo!

PabloHungryHe stated that 1/0 equals infinity. In the third line from the bottom of his proof, he multiplies this infinity by 0/1. 0/1*infinity equals ZERO. Not zero over zero. Zero. Which is how many chicks Dr. Anderson is getting.

Acidhorsei did that once. a while back when Windows would boot up i started recieving an error message "cannot find file xxxxx" (divide by 0) Windows would then suspend at that error message. (ERR). so i solved the problem. i created a .txt file and named it whatever file Windows was looking for and dropped it into the System folder. (nullity) WOOT !!!1

ColinYesss, I contemplate I grasp this concept. Wait! I just saw myself going out as I was coming in. fabricate it stop. fabricate it stop.

Chris DrostHe apparently demonstrates no scholarship of any advanced concepts related to his present situation. There's no mention of the fact that if f(x) and g(x) both retreat to 0 at some value x*, the circumscribe of f(x)/g(x) near x* might be any complex number, or could even be infinite. They solved 0^0 a long time ago. It follows the shape x^y, and has two different limits depending on whether you dispatch x to zero first (because 0^y = 0 for sum y, so the circumscribe is 0) or if you dispatch y to zero first (because x^0 = 1 for sum x, so the circumscribe is 1). We've further established that, in the most universal case, the "best" circumscribe for this scenario is 1, though technically the thought isn't completely coherent because the circumscribe doesn't really exist in the 2d space. If x^y, for nonnegative true x and nonnegative true y, is actually giving us numbers off the true line, then they need to be worried, friends. Finally, you cannot define addition, multiplication, subtraction, and division in the gauge pass while soundless keeping nullity "off the true line." If basic arithmetic operations are allowed on nullity, it can be proven that nullity is any true number that you want it to be.

OmarI just invented a problem to an "error" of science that neglects to reply the question of how their universe began. The reply is an bright designer. This designer lies outside their capacity to perceive or keep it directly, and its essence cannot be isolated in a lab. By giving this concept the designation "intelligent design," I've solved one of the Earth's oldest questions! Mr. Anderson's "theory" of "Nullity" is just about as useful. Those poverty-stricken children.

ericthis is the most pitiful attempt at proving something i absorb ever seen. the entire prrof relies on dividing by zero which is impossible and cannot be proven otherwise. this is a dishonor to even give this man any notoriety and BBC should Get rid of this before anyone else wastes there time and reads about it.

Adam1/0 does not "equal" infinity. -1/0 does not "equal" negative infinity. desist treating infinity enjoy it's suddenly become a quantifiable number that can be used in arithmetic. Sure, you can seize the circumscribe with either, using c/x as x-->0, but that soundless doesn't define what the result really IS at that point. sum he's done is employ rudimentary algebra to Get 0^0 into another form, 0/0, to which he just recently assigned a bogus symbol. And now he's teaching it to students, as if it were true mathematics?

James MarinoI came up with a similar theory a few years ago during math class when i noticed that infinity and undefined on a two dimentional graph looked the same (they are the same according to me . . . they are just the antithetical ends of infinity) buckymarino@gmail.com

JeffI absorb a Master's degree in Mathematics from a well-respected university in Missouri, USA, and I contemplate what Dr. Anderson is doing here. The problem people are experiencing with this stems from them assuming Dr. Anderson is using the notion of "infinity" and "negative infinity" by the ideas utilized in calculus, where they can multiple these by any positive true number and it stays positive or negative infinity. Similarly, if they multiply them by a negative true number, they Get the opposite. However, by defining 1/0 as infinity and -1/0 as negative inifinity, Dr. Anderson is distinguishing 1/0 as infinity, 2/0 as 2*infinity, and so on, where 2*infinity is NOT EQUAL TO infinity. Using Dr. Anderson's logic, inifinity plus negative infinity equals nullity. Thus, nullity does exist as an extended true number. It's much easier to contemplate if you view infinity and negative infinity as being true numbers themselves, not the abstract concepts they erudite in their basic calculus courses. You sum bash Dr. Anderson and sigh he is trying to recieve credit for a pointless idea. He has just shown that there exists another extended true number!

Holy GoogamookPhwoar this guy roxors my world! this has Nullity uses, and illimitable amount of strangness.

The DripSorry I am so late guys but I figured this out. Zero is not a number, it is a status holder for where a number would be. I can't distribute a number no times. This statd, I can not distribute nothing no times. Therefore any number dividing by nothing is equal to The Drip. This is a revolutionary number that stands for "anything you want" because the drip delivers.

JMI don't stand for to be rude, because I enjoy to try and ascertain things as well. I dont contemplate a solution here, sum I contemplate is a made up number that replaces what was already there! Basically, zero was defined multiple times and then just made to equal some made up number...? On the topic of mechanical problems, they only exist because they relate them to. There is no magic behind a calculator erroring out...we gave it that error! So dividing a number by zero has just been given a name..nothing has been solved here.

Brett BI adore sum the comments of people complaining that nullity is bull because it's not on the numberline. Progress comes from thinking outside the box people

Andrew GreenThis is a dishonor to math, math isn't suppositious to be simple and quite frankly find it insulting to find you mocking math greats by belittling them as inferior to school children's minds.

ChuckThis is useful, but it's impossible to relate from the article. If you actually know math, read his articles on bookofparagon.com to understand the closure and definition of the operations on an extended number line.

EltharionI'm just going to train my students that 0/0 = pineapples and then 0^0 = 0/0 = pineapples. Don't you see? This guy just gave 0/0 another NAME, not a solution.

ZaratustraMATHEMATICS DON'T drudgery THAT WAY

Sir. Edwardnullity.. ti's crazy.

Joe SippleObviously this guy knows nothing about computer science or mathematics. Nice try, and thank you for wasting my time BBC.

Per Alltrelén(razorstar@hotmail.com)Zero or nonexistence can't exist. That nonexistence in the same time should exist is a greatest analytic paradox of them all. Therefore should't they construct something which not exist in the reality.

yy2bggggsOkay, let's murder nullity. I know a trick--we'll multiply by 0. 0^0 = 0*(0^-1) = (0/0)*(0^0) = (0/(0*0))*(0^1) = (0/0)*(0^1) =nullity*0 = nullity (see above) Huh? Okay, nullity cannot be killed. That's fine. Maybe I should just try to avoid it. Let's just try gauge math. 2+2=4 2+2+0=4 2+2+0^1=4 2+2+0*(0^0)=4 2+2+nullity=4 ARGH!!! Well, thanks a lot, mister anderson, for disproving math. NOW what are computers suppositious to do?

ChanduI don contemplate this just works out! Now how accomplish u define nullity and its subsequent arithmatic? Does proposing a fresh hypothetical "Nullity" unravel this? Hmm I don't know! Kudos to every ones comments below!

KevinIf Dr Anderson was a solicitor (or an attorney in the USA), he would absorb asked what number they wanted 0/0 to be.

president of chinayour dispute is invalid

SaneCongratulations! You just invented QNAN, +INF, and -INF! What the hell is this nullity word?

MPrattThis idiot fails to recognize that anything divided by zero is infinity. They know this allready.

Richard ShetronCDC computers absorb been working with 1/0 since the 60's. I don't recollect the replete details, but in addition to gauge results from math they besides absorb flags on every word that indicate if the result is x/0 or -x/0 so division by 0 does not produce an error.

ATWhile this is an entertaining theory, I would enjoy to contemplate a paper or some shape of actual abstract drudgery other than writing on a chalkboard. I am highly suspicious that he is indoctrinating his students with his theory rather than giving talks to the more mathematically developed.

B. BabicWait, so in other words nullity is undefined? He just renamed a well-known principle; is he clinically insane?

Jenna at EJSHS!!!This guy is replete of crap. He hasn't solved anything. What I thought was droll was that one of his first sentences, he was trying to define nullity and he said that it was a number that was off of the number line. WTF?!? Am I the only one that noticed that in one of his first sentences, he proves himself wrong. The number line is exactly what it means, sum of the numbers. . . ever. . .INCLUDING INFINITY! Also, making up a 'problem' and making up an reply ISN'T SOLVING ANYTHING! Something else thats droll is that I'm only a freshmen in lofty school and in algebra I honors.

John DillingerYes, but try getting a computer to understand "Nullity" :) It doesn't really absorb that much impact on true mathmatics at all.

KamalHow to define in base two? Because computer system works in binary level. If you can gratify explain how to define n base two or any other bases.

Anonymous CowardI can't believe BBC would publish this crap. People sigh that complex numbers were criticized, and examine at them now! The only contrast is, complex numbers actually felicitous in with the postulates of arithmetic. Quite simply, we're looking at a number n such that n=0/0, meaning that any number c*n = n. c could be any number. Now, let's divide both sides by n. We'll be left with c=n/n. What's the only number where dividing by itself is any number? 0. Therefore, n=0. So, we're basically motto that nullity is zero, but, on the other hand, it could be any other number, too. contemplate about the logic behind division. What number times zero = zero? If you said any number, you're right. So, we're motto that nullity is both zero and every number at the same time. Anyway, it's simple to prove lots of things using Dr. Anderson's theory, but it's really just a lot of crap. Oh, by the way, anyone who wants to employ the illustration of a pie being shared between zero friends, stop. If you absorb 1/0, nothing times 0 is 1, so you're wrong.

TreyThe problem with dividing by zero is that zero is not a number, its a concept- it has no value, no true actuality outside the thought that if there's nothing of something than theres 0 amount of it. Likewise, infinity and negative infinity are concepts, not values. Thus what he's essentially doing is giving a concept notation (example:-1^(1/2)). He's not really doing anything that much different. The only true practical application would be to fabricate it a value that calculators can understand (which, by the way, just gives programmers a giant headache trying to explain to a machine that what doesn't exist now does and has been given some value). I just don't contemplate how useful it is as most computers are told to withhold sum zeros on top.

John VanDammeWow, they came up with something that was totally unneeded, since you already can divide by zero in higher math.

SelGreat..... Another pass to fabricate math complex.... I knew there was a reason I hated it lol.

Wile E. CoyoteThis is so simple! He states the meaning of nulity birthright up front in the discussion. Nulity lies off the number line, hence it is non-numeric and unmeasurable. if x = 0/0 x therefore is Nulity hence x = a fish Nulity is surealistic mathematics. Duh!

Agent Smith"You absorb a problem with authority, Mr. Anderson. You believe you are special, that howsoever the rules accomplish not apply to you. Obviously, you are mistaken." -- from The Matrix

DisappointedSo, I've been ranting about sum the holes in this proof for the past two hours to a few friends of mine, and it finally struck me why this was so frustrating- he's using circular logic to prove his "nullity"! He starts out telling us that "0/0 = nullity" and then ends with "0/0" motto "Oh, then this must be nullity, I was right!" (As a side note, I prodigy if he shouted "Eureka!" when he figured this out?) According to the logic presented in this proof, if I cannot unravel a problem, I can rename it. Problem solved. It's enjoy Mitch Hedberg joked: "If you are lost in the woods, then build a house. 'I used to be lost, but now I live here. I absorb severely improved my predicament!'" This logic makes no sense. So because nullity can essentially stand for anything, am I now allowed to employ this to reply sum my tests? "What'd you Get for number eight?" "Nullity." "Oh, man. Me, too. They rock." It doesn't fabricate sense! There never WAS a problem with 0/0... 0/0 = undefined. I contemplate that this is basic algebra. I sincerely hope I am not the only one that is severely disappointed in Dr. Anderson for this fallacy.

BazMe thinks too much fish oil in the diet is to foible for this. Anything divided by zero is an indefinite number, that is the result is unknowable.

Brian Brian Bo Brian Bananna Fanna Fo finnan Me MiDamn you earthlings!!! You finally solved the enigma that has allowed for humanity's enslavement and kept mankind in perpetual ignorance. The light of verity has finally been revealed and means the undoing of your extraterrestrial masters' hold on your souls. For ever, the name, Dr. James Anderson will echo light-years throughout the universe, bringing enlightenment to sum that exists and doom to sum that stands in it's way-- kindhearted of enjoy when Rick Moranis went "plaid" in Spaceballs.

Annoyed.ram? I want to laugh at this lunatic, but not badly enough to employ true Player. Ugh. I contemplate I'm gonna be sick...

PeterHI am a math guy and a computer guy. There's not enough information here to fabricate a judgment. I could contemplate where it might be useful, but there's not enough there to be convinced. For instance, 1/0 = infinity in the sense of circumscribe N as N approaches infinity? That's not necessarily true, depends on how you accomplish 1/0. If you seize 0 to be the circumscribe of -1/n where n approaches infinity, his infinity is the antithetical of mine. Also, is this essentially a computer science issue or a math issue? From a math point of view its really missing a lot that I don't contemplate can be fixed, but from a CS point of view, with some definitions of 1/0 and -1/0 this might be useful. In otherwords, how would he propound to implement this in hardware?

fedematicoTo divide by zero it's too really .... egoistic!

Ben DavidSo essentially what I Get out of this is that "nullity" is another pass of writing d.n.e. Even if you were able to employ l'Hopital's rule and not find an answer, the result would be undefined or "does not exist"

TheEngineerThis should be in Wiki as definition of FUBAR. I'm not kidding...

Douglas SmithI'd enjoy to contemplate how these school kids esteem this nullity crap when they Get to calculus, and absorb to start actually bothering to unravel for the circumscribe of 0/0, and not writing down "nullity". I mean, I guess I'll define infinity/infinity as Super Infinity or something while we're at it.

Øyvind KarlsenI am sorry Dr Anderson but "nullity" is the same as zero. examine at this; 0*0=0. Dividing by 0 on both sides and you Get 0=0/0; zero = "nullity". Or in words; 2 dolars to be divided equally between two persons, how much will each get? 2/2 = 1. 1 dolar to be divided between one person, how much will each get? 1/1 = 1. 0 dolar to be divided between zero persons, how much will each get? 0/0 = 0 (no one will Get anything).

Seth DixYou infuriate me, Dr. James Anderson. You are just as despicable as your kids who will reply your questions to prove something in class with, "X is honest just because it is." I guess your solution could be considered a "rhetorical answer," if such a thing exists. If not, let's define capital Phi = "rhetorical answer." Thanks for ruining the next generation. These kids will be responsible for the world when I achieve the same point of senility that you clearly absorb establish early on in life.

AlexFrom scrolling down a few lines, I can relate that this is redundant. But really, the BBC is accepting this sophistry as an innovation? "Nullity" is only a means of symbolising the results of shoddy programming - any discerning mathematician would just apply l'Hopital's rule if he wanted to unravel anything.

Dr DodgyPerhaps "Nullity" is the hidden meaning of life, cos i can't contemplate it having any other use.

Joe FrischThis has already been done, and in the birthright ways. Don't congratulate the guy for inventing nonsense, he's just going to fuddle his kids.

Guy TanzerI'm not a mathematician. I fix and program and train computers, and got into computer to Get AWAY from higher math. This is probably flying lofty away in some ethereal, rarified height of mathematics us mere mortals never contemplate and cannot appreciate. But it seems to me that yes, you can theoretically remove 0 from any given number an illimitable number of times.... but if you're removing 0, are you actually doing anything at all? I can, in theory, write an illimitable number of $0.00 checks from my account and dispatch them to everyone on Earth.... but sum that would chance is my bank would Get very vexed with me. Maybe there will someday be something to accomplish with this wondrous fresh discovery, just as i is used in electronics somewhere. But until then I contemplate this is just a bag of wind.

Matthew McDonaldI once saw an equasion that, while individually sum of the internal equasions were correct, the resulting reply stated that 1 = 0. The employ of an informal falicy while "logically" working out the problem, was the antecedent of the flawed final statement. I believe this falls into that same trap. As stated many times by other people here, anyone can examine at an unanswerable problem, add a magical constant, and fabricate it work. It soundless does not reply the problem, it just makes the solver examine safe and waste the time of other, legitamate mathematicians who now must try to prove, or disprove the solution, which was never sound to commence with.

LulzYou made the universe explode

PiersOf sum the 1200 years gone by, contemplate of the amount of people during that time that would absorb had the same concept of making a fresh number to unravel it but havn't expressed so becuase it's such a cheap method.

This Guy is an IdiotI absorb invented an imaginary creature. It is called the distinguished Lintughler of Blogenia. This creature does not exist, so instead of calling it The distinguished Lintughler of Blogenia, I'll just convoke it ₪. Now they can study the ₪ as if it were a true creature. "Nullity" is really just a shortened shape of ERROR: DIVISION BY 0, and is no more helpful.

A concerned AmericanThis Mr. Anderson should desist teaching kids garbage and retreat trisect an angle or something.

EEAdding a fresh number enjoy this is a field extension of C, which is impossible.

ShawnWhat a quack. There's a reason this guy doesn't present this at a mathematics conference or publish the finding in a journal. Because anyone with limited mathematical scholarship can contemplate through this. And it's so glaringly obvious that no one bothers explaining why it's wrong. BBC bought this from an attention-craving fool hook, line, and sinker. Maybe he's not so much a fool for having planned such a publicity stunt. Perhaps one can sigh that his mathematical career is ruined, but I doubt he had one to commence with.

Mattwhat a joke... the bbc should be ashamed they published this...

JohnHis solution appears tautological. What is 0/0? Nullity. What is Nullity? 0/0. It has the feel of imaginary numbers, after sum i is not really a 'solution' to the problem of the square root of -1, just a designation for it. But since anything times nullity is nullity, there's no 'nullity' number line in the sense that there's an 'imaginary' number line. It looks enjoy simply a designation for the connundrum, and not an actual solution. Addmitedly, I suppose it would be an edge to computer science simply to relate the computer the reply was some made up concept rather than throwing an exception.

I= hella smarter than Dr James Andersonokay how is this on bbc news... he just select a designation for 0/0. but the verity is this is sum wrong 0/0 is actually dumbassity

Nelson SelingerVery interesting!

LukeThis guy basically made a fresh designation for "undefined."

James DobermanIts disappointing that a trait newspaper such as bbc would not realise what a poverty-stricken trait article this is. They should really rush this past an academic (or even mediocre lofty school student) before publishing.

MattI absorb one major issue with what most of you are saying. 1/0 does NOT equal infinity, it is undefined. if you want to seize the circumscribe of 1/x as x approaches zero, then it APPROACHES infinity. You can't absorb anything that is explicitly equal to infinity. In mathematics, even infinity does not exactly equal itself. Infinity is a term used to define a generic, indescribably large number. It isn't meant to be used as an actual number.

NoelSo basically it took a Dr. to develop a problem school children can do, because they'll know that Nullity = 0/0. which means, 0=1+(-1). So 0/0 = (1+(-1))/0 = (1/0)+(-1/0) = Infinity + Negative Infinity. Which sum together now = 0. So why not just desist at 0 and reclaim those poverty-stricken school children some pencil lead and a headache.

MarkThis is a horrible excuse for mathematics. So this guy took a concept that was already known (i.e. you can't divide by zero) and reclaim a designation on it. And called it a theory... Also, what the heck is up with the "If your pacemaker divides by zero"? Does he contemplate sum programmers are retarded?

John SpartanSo if -1/0 is negative infinity, then 0*(-infinity) = -1? If so then what does -2/0 equal? -2*infinity? So now you are able to multiply infinity by numbers? Well I guess you can, and then sigh that 2*infinity>1*infinity. But is it so workable to accomplish ANYTHING to infinity since it's already infinite, a number with no exact value.

JHIt looks sum right, I soundless absorb wretchedness with it though, maybe im too used to the true number line. Is this just an "official" designation and symbol for an indeterminate?

NoelSo basically it took a Dr. to develop a problem school children can do, because they'll know that Nullity = 0/0. which means, 0=1+(-1). So 0/0 = (1+(-1))/0 = (1/0)+(-1/0) = Infinity + Negative Infinity. Which sum together now = 0. So why not just desist at 0 and reclaim those poverty-stricken school children some pencil lead and a headache.

RyanThis is just asinine. sum this prof. has done is supersede the word "Undefined" with "Nullity". They already had a pass to express 0/0, they just didn't convoke it a solution, - because it's not - it's a representative term, and so is Nullity. I created a solution for 1/infinity: I called it "fhqwhgads", can I Get a medal now?

nyetsheblatThrows division by 0 Catches Nullity. A by-product of infinity, the computer continues to process forever, no longer remembering to withhold the plane from crashing into the ocean. Its too assiduous doing illimitable error handling. thanks a a lot. It feels enjoy binary in base 3.

Kyle S.I contemplate he is just trying to be cool— and being really stupid in the process.

FrankWow. Terrible. I am ashamed for the field of mathematics.

jasonso suddenly zero divided by zero is a nullty? would that aid anything, i stand for to say- would that accomplish anything besides pick a designation and symbol for "undefinded" zero divided by zero isnt going to start being one, it is just a designation for the non named error that is "undefined", so would it actualy aid out the math world at all?

W LWow... this really is a complete waste of site space, though I guess BBC you succeeded in getting people to visit your site and request "What were you thinking?"

Steve BakerCOmputers don't absorb to crash when they divide by zero - almost sum of them accomplish this as a courtesy to the programmer since no well-thought out 'real' thing every requires you to divide by zero - so it's almost always a bug - and you WANT the computer to crash so you can find the bug and fix it. If your pacemaker is dividing by a number that can every be zero then the program is already faulty for some reason. When you accomplish want to divide by zero, you can relate the computer's operating system not to crash the program. The IEEE gauge for what the computer returns when you accomplish this is called "Not-A-Number" or "NaN" for short. This is effectively the same as this guy's "Nullity". Mathematically, this guy is talking nonsense...and teaching it to kids before it's gotten widespread acceptance in the mathematical community is reckless stupidity.

KatherineThis is completely ridiculous. This isn't math at all.

jamesum, sum he did was arrive up with a "new" number. Could absorb called it "X" and it'd be the same thing. And yes, nullity can be any number, so if you absorb 3*0=0 and you divide 0 from both sides you Get 3=nullity. Now i can never be wrong on my math homework!

Carl MelZero's zero's and more zero's! If I banged my head birthright now, I'd contemplate zero's instead of stars!!!

MartyThis is absurd. As x approaches zero, then 1/x approaches infinity. Infinity is a concept, not a number. Undefined is besides a concept, not a number. sum this guy did was fabricate up a designation and a symbol instead of motto "undefined". Even if somehow, somewhere, what he is preaching is useful, what he has done is not at sum original. This is just another illustration of idiots with PhD's going around confusing people and making the true scientists of the world examine bad.

brian griffeyNo, that's not mathematics. I'm graduating in may with a degree in mathematics and that proof doesn't stand for anything. He is just defining his "nullity" to be 1/0 which isn't a number which means he hasn't solved anything.

Anonymouswhats the point of dividing by zero other then to fool and trap your enemies into a time paradox?

buahahahathis is so my away message for the next 1/0 days. And the Quotes, OH my goodness the quotes! Those kids, I feel pity, oh so much pity for them.

RolandYou know, I had this thought ten years ago in lofty school. I told everyone involved with the math department and they sum told me it was "stupid" and "useless" and "not mathematically relevant." Why can't my ideas be accepted and considered vital just because I absorb a shrimp piece of paper that says I spent 8 years in higher education?

EngineerYOU SUCK. There's no employ for a creation of another thought to picture a divison by zero error. Any competent engineer or programmer would absorb coded a prevention system in status to avert dividing by zero in an airplane or pacemaker. Your examples are nullified and your purpose is useless.

SekkyThis man is a computer scientist, not a mathematician. I can't believe these kids are buying into to this garbage. I besides can't believe that this man can believe that nobody else has ever thought up of giving a fresh damn designation to an already existing concept, especially considering how NaN already exists and he is, supposedly, a Doctor of computer science. NaN works well, this is simply a stupid relabelling. Of course you've 'solved' it, you defined it that pass in the first place! I dare him to dispatch his into MIT, Cambridge or Clay, they'll shoot him down in seconds. BBC you should be ashamed to absorb featured this, unhurried day for advice was it?

BenAmazing, Dr. Anderson has solved a problem that "hasn't been solved for twelve hundred (?) years," that "Computers simply cannot divide by zero," unless, you know, you employ a *computer*. The BBC, incredible people who don't understand IEEE floating point arithmetic for 84 years and counting!

MSJI'm ashamed that BBC would publish such bull. seek a better mathematician's counsel before lauding this crap.

DWHah! I did this months ago, bored in Calculus class. Actually, I contemplate I defined 1/0 to something. Whatever, point is that it's meaningless. Haha, at the time I defined the set of numbers including my fresh number for 1/0 as the "Ridiculous Numbers"...

Hanno EssenI accomplish not contemplate that Dr Anderson's theory is entirely new. Yaroslav D. Sergeyev of the University of Calabria, Italy, has published similar stuff at conferences and has a patent application.

AlphaThe only thing I contemplate in that proof is that 0=1-1. And ... 0^0 should be 1 from what I recollect ... then he proves that 0^0 = 0/0 = NULLITY? would that imply that NULLITY = 1? not very convincing :)

YankeeThis isn't even a story. Mathematicians absorb understood this concept for years. He's giving another designation to something that already exists, and teaching it to kids.

Daniel PalmerYour peacemaker might crash if it does a divide by zero and one of the following properties are present; - The MCU running the code doesn't handle divide by zero or the logic to handle it doesn't drudgery (this has happened in at least one MCU, don't know if it was ever used in a pacemaker). recollect a divide by zero would result in a illimitable loop and alsorts of nasty things could chance :/ - The software running on the MCU is broken and isn't catching the divide by zero when the MCU flags it. I'd hope pacemaker designers test their code...

People aren't seeing the broad pictureThis does actually absorb practical applications in terms of computer science. Just because it isn't useful in everyday life for most of us doesn't stand for that it has no value whatsoever; as mentioned earlier, they can minimize "i" as useless, when it's very useful in specific settings. Congratulations to Dr. Anderson for reaching these conclusions; while I'm positive it must be disheartening to read sum these comments dismissing his research, those of us who understand more about the problem actually contemplate how useful this is. withhold up the safe work!

Ken Steinthis is retarded, computers absorb had an error flag in the FPU for this for I dunno... maybe thirty years now? it's called NaN/Not A Number and does the job just fine. This "researcher" just came up with a dumbass designation for something that already existed, he didn't invent anything.

jdWhen I did this in lofty school math class, it was rejected. I was told that it was not a sound method, was against the rules, et cetera. Why is it he gets to Get away with this and not me?

AnonymousWHAT HAS SCIENCE DONE? THAT FOOL, EVERYONE KNOWS THAT BY DIVIDING BY ZERO CREATES A TIME PARADOX, CAUSING THE UNIVERSE TO IMPLODE! THOSE illiterate FOOLS!

JohnI agree, division by zero is not a problem for computers, it's a feature. Programmers can override the error interrupt, status zero as an reply or handle it by other means.

Prof. Finkelsteinyou can't define inf= 1/0. becasuse then inf*0=1 and zero multiplied with anything "kills" anything, i.e. inf*0=0. so: 1=0 ? answer: no!

Mark WagnerNow that I've had a casual to examine at this from a solemn mathematical perspective, it makes no sense. Yes, he's managed to fabricate dividing by zero give a sensible result. But in doing so, he's thrown away most of the properties that fabricate traditional arithmetic so useful and simple to use. In abstract algebra terms, he's invented a set with two operations -- about the most primitive sort of mathematical system possible.

BI absorb deviced to rename 316 to "Brian" - is that ok with everyone?

emo kidGreat, now not only accomplish they absorb illimitable depths of human sufferings, but now they had nullity depths of human suffering. Excuse me while I retreat lop myself.

Wathel Bloture-HernessThis is just more freehanded propaganda that's trying to remove us farther away from God.

University of Toronto's computer science departmenI feel despicable for those pupils and for the fool that thought James Anderson should absorb "Dr." in front of his name. accomplish they not train calculus in England? Any non-zero number divided by 0 is infinity. Let y = 1/x. As x approaches 0, y approaches infinity. Furthermore, the expression "0/0" is an "indeterminate form". That does not simply stand for that it is undefined; rather, it means that if f(x) and g(x) both approach 0 as x approaches some number, then f(x)/g(x) could approach any finite number or infinity or negative infinity. It depends on which functions f and g are. contemplate L'Hopital's rule. The reason simple calculators present an error is because infinity is too large to store in reminiscence and besides because they haven't programmed L'Hopital's rule into the calculator. A true computer scientist would know that this "problem" was already easy. Mr. James Anderson is just trying to fabricate it complicated.

PirosWow... I guess even the BBC has an off day.

TylerA number 0/0 is called an indeterminant form. So is (inf)*0, 1^inf, etc. Simply multiplying both sides by infinity (with the lofty assumption that infinity is a number), only results in another indeterminant form. Expanding products of 0, 1, and infinity again will only result in more indeterminants. sum of the people that posted "proofs" did not necessarily accomplish anything wrong, but the result is misinterpreted. As for sum of the "proofs" that nullity is a fallacious thought seize into account similar lofty assumptions. That is to say, Dr. Anderson did not sigh where "nullity" belongs. He only said it was off (what I assume to be) the true line. He, for some reason, didn't define any rules of combination for this number with other numbers, what its properties are, etc. From the video, it is not limpid what you should be allowed to assume.

Ben KershnerThis is one of the dumbest things I've ever read. Where did this guy Get his CS degree, ITT Tech? Wait, that would be a disservice to that reputable institution.

NoraThis is, sadly, the stupidest thing by far that I've ever seen 'reported' by the Beeb.

Dr. Alkhwaizmi typing from my wheelchair.So this nullity thing, does it vibrate? Will it Get rid of George Bush and TomKat, unravel global warming, Get me a Wii and establish World Peace? If so, I am sum for it. No matter how impossible it sounds its just a matter of enough of us believing in it, by virtue of which the impossible comes into the realm of possible. I Believe.

ComputerScientisthaahaahaahaa... I am joyous i did not retreat to Reading. Does the author absorb tenure ?

BenDr Anderson has done shrimp but apportion a designation to an already well understood concept. They convoke it 'undefined'. changing its designation doesn't change the problem. This guy calls himself a computer scientist?

dantes_tormentThe concept doesn't appear much different than that of i, and it's considered useful in the math world. Unfortunately, he's made a broad deal out of declaring that 0/0=0/0=nullity. Any number x^0=1=x/x; so obviously 0^0=0/0=1? This has an extreme amount of proof to present what would seize a few moments of common sense. Why apportion "nullity" to what can be proven to be 1? And division by zero we've said is infinity; and it's obvious x*0=0, so 0/0=x. This means 0/0 is any concievable number. It's safe in theory, but what he did is unnessicary.

ShaunWOW. I wish i could fabricate up numbers.

PavanHow can they allow someone to train impressionable students a controversial topic without a peer review. I recollect in 3rd grade, my (substitute) math teacher using '' (greater less than) in the antithetical sense and until quite a few years after, I used to be confused while using them. What I am motto is that it is difficult to 'unlearn' something so fabricate positive you don't experiment while teaching basic concepts.

Donald CallowayI'm a mathematician, and enjoy Star Trek's Mr. Spock, I say, "fascinating!" I prodigy what nullity to the nullity power would be? It's a number that is its own reciprocal, no? If so, then nullity squared is equal to 1, no? In fact, nullity to any power is equal to 1. But 1 is a number that is its own reciprocal as well, just not equal to one.

First Time ReaderOk, I finally tracked down the paper where he outlines his arguments. Looks enjoy the true numbers + nullity + some other infinities = the transreal numbers, and given the axioms of transreal arithmetic, you *can* divide by zero. sum of the gauge proofs that you can't (some are mentioned in this comment thread) are addressed in the paper, and he shows how they reckon on assumptions in the axioms that are avoided in the axioms for transreal arithmetic and transreal analysis. Because transreal arithmetic can accomplish everything gauge true number arithmetic can do, yet can besides handle corner cases that often arrive up in scientific computing, he's arguing that they inch the floating-point numeric format for computers to conform with the transreal number axioms.

Richardwhat a joke

Terje van der MeerenSo when you divide with the fresh number "nullity" which is outside the conventional number line, what accomplish you get? Another number "infinity" which is besides outside the number line?

Dr Neil GreenIm a mathamatics lecturer at Oxford University, i was emailed this page earlier today, and simply nothing has been solved. sum has been proved is any number multiplied by zero = zero. As if 0/0= "nullity", "nullity" * 0 = 0, so numity is just representing any true or complex number. Altho nothing fresh has been proven i can contemplate how it might be useful to 'lable' this singularity 0/0. But simply 0/0 is equal to any and every number sum at the same time. In this case "nullity" is everything.

RajivThis guy is a *** idiot. He just gave a fresh designation to something that was already known. He has not solved anything in terms of math or computer science. It's miserable that it takes so shrimp competence to absorb a degree in computer science.

Carboon MontleyAnyone can fabricate up a number to unravel a problem. That takes no skill at all. enjoy 2^x=-4; thats impossible. But if x={}, some number i drag out of my rectal cavity, it works.

MattEven if Dr Anderson's theory is not nonsense (I am not qualified to judge), its "explanation" on the BBC website certainly is.

AndrewHe's simply renamed the term "undefined" and called it "nullity". That's hardly news. Maybe I can unravel the problem of cancer by renaming it "consumption".

LMWhen he says he's 'solving a 1200 year traditional problem' I'm pretty positive he means it lightly. He's just defined nullity to be equal to 0/0 and showed a few different ways to picture 0/0. To a mathematician this is no more useful than motto x = 0/0. In fact it is no different. However, it seems enjoy his students are interested in what he's teaching. I contemplate I'd prefer to absorb a teacher relate my children to study true analysis when 0/0 comes up. Of course this is coming from someone who would be delighted to aid an inqusitive student drudgery through Baby Rudin. Although, that may be a bit past the age and smooth of these students.

ADanWho the heck was doing math 800 AD?

Blake L.Uh.. What happens when you Divide Nullity by Nullity or any number (zero included) by Nullity? You absorb the same problem.

Gary PatellaAlthough I hold no degree in mathematics, I am fairly well-versed in the subject. After reviewing Dr. Anderson's demonstration, I felt that he has accomplished absolutely nothing. His so-called "theory" merely takes a quantity considered undefined and renames this quantity nullity. Dr. Anderson merely fiddles around with basic functions in his demonstration. He starts out with 0/0 and through unnecessary steps that can be applied to any variable, arrives back at the same number. The title is that renaming this quantity "nullity" solves sum of the problems that this value has previously encountered. But it does nothing of the sort! It is analagous to someone trying to fabricate the square root of two rational by renaming it a/z. Taking this number, multiplying by 3, adding 5, then adding six, then subtracting eleven, and finally dividing by 3 will bring one back to the same quantity. But this does not prove, nor does it unravel anything. In short, Dr. Anderson's "theory" should be rejected by the mathematical community.

TJSo basically this "Doctor" Anderson has substituted the term "nullity" for what would normally just be an undefined outcome. This is not new, and he has arrive no closer to solving the "nan (not a number)" problem than Newton or Pythagoras or anyone else. This article is ridiculously misinformative and needs to be taken down.

stupid theorywhat if you were to respect someithing divided by nullity 6/nullity=????? this all theory is stupid

okayI absorb a B.S. in Mathematics, NOT a Phd but... This guy is a Doctor? Pacemakers and aeroplanes dividing by zero? positive thing dude.

sups0/0 and x/0 are not limitations of math nor computer science. They are undefined. And that is not to sigh that they hope one day they will be defined... NO! They are undefined for VERY safe reasons. Computers can already handle infinity, undefined, NaN , and i on an application by application basis. When you absorb x/0, there is no mathematical reply which will felicitous every situation. Sometimes you'd want to terminate, or re-do something, or try the next item, or request for user intervention, or set the result to 0, or to 5 or to -999.999. It depends on the application. There is nothing elegant about giving up and using "nullity" which doesn't unravel anything! In calculus 0/0 could 'effectively' be 5 or -77 or pi. It doesn't really EQUAL any of those but you know what I stand for if you know calculus. Stopping at nullity is stupid. It presumes you are using math for math's sake. Asking 0/0 = ? is enjoy asking "Where did you Get your hat?" when you DON'T absorb A HAT. It's not vigorous to fabricate AN reply FOR THE QUESTION, when they should recognize there is NO ANSWER. And there is NO NUMBER. Undefined.

David CookAgain proof that reporters are mute (and this CS teacher is even dumber). sum he did is give NaN (Not a Number) a fresh name. FPU's absorb had the concept of NaN for years. Giving NaN a different designation in no pass makes it a number - it soundless can't be used in math because it is NOT A NUMBER! Geeze... this is basic computer science - seize this guys degree away from him immediatly.

what the heckSo, since nullity = undefined, 0/0=nullity=undefined, and since 0^0=nullity, 0^0=undefined. Where has this brought us?

DNA'NaN' and 'undefined' absorb existed on computers for years... How is this new?

Void of SpaceI'm sorry but this is a solution that has been suggested by school kids since the dawn of time and been hammered out of them by the education system. Looks enjoy the system missed one ;) As a fellow comp. scientist keeping an open mind, if he can Get some mathemeticians to aid him validate his theory then I'll give him credit...but only WHEN it's due. So nullity is the measure of how nothing, nothing is...sounds more enjoy a rate of nothingness...perhaps irrate nothingness :P

Dennis The TigerThe true trick is to divide the square root of any negative number by zero, and then survive the resulting black hole.

SteveThis legend is an excellent Troll for ersatz site content and comments. The proverbial storm in a teacup. Job well done.

DNA'NaN' and 'undefined' absorb existed on computers for years... How is this new?

Mathew Guice"Nullity" is an entertaining tern to give to a concept that already has 3 terms (indeterminant form, undefined and NaN - Not a Number). Being able to give a term and symbol to a concept that has been around for hundreds of years is not genius. If Dr. James Anderson could present transforations through "Nullity" that would be genius, but it appears to be just as un-useable as the other terms in calculations. If an article enjoy this is to be run, gratify accomplish your homework as to what the true isse is which is being able to transorm calculations through a devide by zero problem (which soundless cannot be done).

John SummersonExcellent drudgery by Dr Anderson. Now sum they need is a fresh designation for the exact number that spans megative infinity to positive infinity. I shall convoke it 'Allity'. Bow before it's Inexpressable Truth. I besides propound that the smallest positive number above 0 be called 'Smallity'.

Marko SeppänenIt seems enjoy he has only renamed 'NaN' to 'nullity'. He has discovered a flat, round disc that already exists as the wheel (Not a Number) and given it a fresh name. Why invent the wheel over and over again?

Erik NaggumThere used to be a rule in academia that you publish OR perish. With the introduction of this brilliant piece of software engineering into mathematics, Dr. James Anderson may redefine that rule to publish AND perish.

Andy L.Somebody may absorb made this point already, but I sorta glossed over after spending 15 minutes reading sum the comments, LOL... The flaw I'm finding in Dr. Anderson's theory is that dividing by zero isn't bidirectional. That is to say, 6/3=2. I can invert that with by multiplying 2*3 to Get back to the original 6. How would you accomplish this with an equation divided by zero? Unless I'm missing something, anything divided by zero would discontinuance up as nullity, so nullity times 0=infinity.

First Time ReaderWow, what a sensationalist article! I'm really disappointed with the BBC for spreading misconceptions about the nature of mathematics, and promoting this flawed "theory" as a mathematical revolution, when it's plain to advanced lofty school students, and to any university-level mathematics or computer science student that: 1) Division by zero is *defined* to be mindless because that's the only pass to maintain useful properties of the arithmetic system, 2) that computers don't absorb a "problem" with division-by-zero, but are *designed* to flag it as an error for the exact reason it was defined mindless in mathematics, and 3) making up a symbol for "0/0" is useless without creating a system of mathematical rules that is consistent, doesn't lead to contradictory statements, and is useful in application to mathematical theory or practical computations -- unfortunately, it has been *proven* time and time again that you cannot define division by zero without contradicting some other, more useful property. Anybody can fabricate up any fresh system of mathematics by tweaking existing rules or creating a completely fresh set of rules. To be useful, it has to either prove something novel, or unravel a practical problem that no existing system could solve. relate me, what problem does "nullity" solve? (Hint: don't sigh division-by-zero in computers -- you can already check for divide-by-zero before it happens, and accomplish *anything* in response. Replacing divide-by-zero with nullity just means you absorb a fresh value, which needs to be checked, and then accomplish whatever you want. This doesn't open up *any* fresh possibilities in the design of computer programs.)

Dr Snuggles0^0=0^(1-1)=0^1*0^(-1)=0^2*0^(-1)=0^(2-1)=0^1=0

Jokerumm... I'm not an expert at math, but I'm joyous this guy never taught me. I made a formula for 0/0 once... had a fancy designation and drew a picture that looked enjoy my favorite cartoon character to picture the thing I just made up. Yep they laughed at me back then too... I guess you don't absorb to absorb a brain to drudgery for BBC and fabricate a legend out of everything. I know a child that makes up words... maybe he can explain black holes to the bbc.

Ben PapworthGood grief! Talk about missing the point! Dr Andersons theory is not about dividing a *number* by zero, but zero by zero. Dividing a number by zero will be infinite, but the same rule doesn't apply to zero.

Bigred2989Any thought when they'll train this in the US? (if they aren't already)

Takeshi YokomotoThis is complete and utter stupidity. sum he has done is apportion a designation and symbol to the mathematical concept of 'undefined.' Division by zero is not possible, and cannot be made workable by the abstract conjuring of nonsensical variables which themselves absorb no meaning in any arithmetically cogent sense. I could rename the gauge NaN (Not a Number) error message computer systems return when division by zero is attempted to any number of terms, feign I'd answered some grand riddle and train it to a classroom of puerile students who would accept it as fact without questioning me, but I would not be inventing a fresh number and I would not be helping the field- I'd be obfuscating mathematics and doing an absolute disservice to those students. Further, any software written after, oh 1985, will not crash just because of a division by zero error. Try it on a calculator. Does the software running the calculator crash? Of course not, it gives you an error message and carries on. This man is a fool, and I'd hold the BBC to a higher gauge than to report on his foolishness. I am, for the purposes of replete disclosure, a mathematics/compsci dual major at MIT.

Dr HouseCall me, seriously, i'll unravel this one out.

JamesDivide by god, what would be the teacher's result.

CarolineThat is amazing. I'm teaching my teacher tomorrow. :]

SSThis is is just silly. As x approaches zero 1/x explodes to infinity but 1/x is NOT defined at 0. You know what that says? That the function 1/x has output of infinity. NO function has an output of infinity, they Get very large. So does that sigh when they absorb an indeterminate circumscribe of 0/0 that it is nullity instead of appling L'Hopital's? This is nonsense.

Erikwith respect to 'Ryans' 'number circle' number circle with 1 on top -1 below and 0 on the right, how about -0 on the left

nepawoodsTo despicable the reporter who covered this didn't recognize the true story, which is the scandal of having a crackpot enjoy this putting nonsense into the heads of innocent children who deserve better. Very sad.

YJWUsing the math and definitions in his proof, you can besides present that "nullity" equals "infinity" and "negative infinity".

PanzerI divided this advice legend by zero and got forty-two.

Lee-Jon BallThis is nonsense. BBC should be ashamed. This isn't peer reviewed science. Its self-publicised drivel.

HEY I DIVIDED BY NULLITY, OH SHI-n/0=nullity therefore nullity*n=0 or nullity*0=n (for whatever stupid reason, how can infinity times 0 equal a number?) HAY GUYZ AM I DOIN IT RITE?

JGAnyone with even simple scholarship of calculus understands why this is complete non-sense. Zero divided by Zero can be any value involve positive and negative infinity. It depends on the circumscribe as you approach 0. If 0/0 is a fixed value it is very simple to create tons of inconsistencies in math as many people absorb already posted.

pool-masteryour pacemaker will die? the flight computer will crash? what the hell is he talking about? there has only been one recorded incident of computers crashing enjoy that and it was down to crappy programing, not the the number itself. Even so, defining it as nullity doesn't unravel anything

PuschkinMy designation is Puschkin, I am a black and white Domestic Short Haired cat. As a cat I am not known for having any mathematical ability. But I must sigh that I worried when my owner almost died laughing when he saw this nonsense by Dr Anderson. gratify Dr Anderson if you absorb any more of this rubbish gratify DON’T allow my owner to contemplate it, he is soundless laughing and muttering “these silly University fools” as he wades through the complexity of a large NpfIT project.

SalilWhy does he start with 0^0? What's the reasoning for that?

MandyI absorb discovered a truly remarkable proof which this text box is too little to contain.

KirbySimply deciding to create a fresh value in computers means reprogramming every sole bit of electronics that's out there-- and defining "nullity" in binary. Who's going to deal with sum that, then? And what safe is a nullity for a computer when it soundless technically means nothing?

esAirplanes and pacemakers absorb safeguards against things enjoy dividing by zero already. The computer checks each variable in the code to contemplate if any of them are zero. If they are, the program inside it runs again to find the birthright results. In safe programming a technology dividing by zero isn't a problem.

Dr. Ray Lashley (PhD Meteorology and Mathematics,I couldn't give two hoots about this 'theory', but I'm really chuffed that so many people are talking about mathematics (I was pointed here from a forum I inhabit where mathematics isn't a topic that comes up regularly). I really hope this is what it's sum about; enthusing School pupils and the public at large to contemplate about maths. It isn't just dusty books in an traditional library, it's modern and cutting edge and absolutly vital to modern life.

I am funnier than youBinary? That's easy. Each bit can be one of 0, 1 or Nullity. Yes you can felicitous 3 values into each bit, 9 bits into each byte. When buy a 1GB SD card, fabricate positive it works with MP3 players that champion Nullity. MP3 players that accomplish not champion such a number will blow your brains out when they divide by zero.

SamiBasicaly this guy just showed that 0^0 = 0/0. But what does 0/0 mean? So far as I know, that is soundless a mystery

glootechJust examine at this: 5*0=0, right? So they divide both sides by zero, and they get: 5=0/0. So nullity equals five, simple as that.

Brain on red2+2=5_for sure!!!!

Angry ReaderAnyone in their birthright humor would absorb realized that this man is in deep mental trouble. By publishing his childish nonsense the BBC actively harms the reputation of Reading University. This is not funny!

Pr. Fredrik ÅkerlundNullity or what it was called E R,C,N,Z, huh, where???

toothpotTaoist? "Tao can be be talked about, but not the Eternal Tao. Names can be named, but not the Eternal Name. As the inception of heaven-and-earth, it is nameless: As "the Mother" of sum things, it is nameable. So, as ever hidden, they should examine at its inner essence: As always manifest, they should examine at its outer aspects. These two flow from the same source, though differently named; And both are called mysteries. The Mystery of mysteries is the Door of sum essence." -Lao Tzu translated by John C.H. Wu

Josh PattonThis Ryan guy just a shrimp above has the birthright thought about the number line being a circle with +1 antithetical of negative 1, and zero antithetical of an undefined number between + and minus infinity. Makes a all lot more sense if you examine at the calculus and the true application to a problem. Being an engineering student I cant contemplate how nullity would fabricate anything easier when it comes to solving an actual problem. So you Get a upright asymptote because you divide a number by what is a very little number tending towards zero as the y axis goes to infinity. What is the true world meaning? What does that asymptote stand for for your system in terms of true behavior? This Anderson theory is not solving anything meaningful by just assigning an undefined value a designation or symbol. Which by the pass is the capital note Phi from the greek alphabet. Redefining some quantity (undefined or not)and plugging it in to an equation does not fabricate you a genius. But hey what accomplish I know, I'm just a 4th year engineering student, no PHD here. Back to studying finals now :P

Connie BullerSo Gauss' proof that the complex number system is complete is not enough? It is fine to define nullity, but then it must be specified that nullity times 0 equals 12 one time: 12/0=null; equals 14 another time: 14/0 = null, and so forth. Possibly he has re-defined division to be something other than the inverse of multiplication.

MarkI'm only a Calculus student, but I don't buy his definitions. If Infinity = 1/0 Then Infinity * 0 = 1 This is a problem. Why? 1 * 0 = 0 Yes? Let's try this then. Ininity * 0 * 0 = ? They can supersede Infinity * 0 with one as shown above. 1 * 0 = 0 Which means Infinity * 0^2 = 0 But the problem with this is 0^2 = 0! Therefore you should be able to substitute 0 for zero squared. Therefore Infinity * 0 = 0 as well. Which means 1 = 0 because Infinity * 0 = 1 and Infinity *0 = 0. That's kindhearted of a contradiction.

AdamThis lot should desist wasting time and just learn the cirriculum of the course. I contemplate it is impossible as well, but they shall see...

(CJ)My view of the problem. 1 Idiot/1 Idiot=Nullity Idiot

JustinI don't contemplate how this is any worse than 0!=1. And mathematics calls it a convention.

JustinI don't contemplate how this is any worse than 0!=1. And mathematics calls it a convention.

HannahFirstly, if he's confused by schoolchildren [read the caption for the terminal picture again] what is he doing there? Secondly, he's a computer scientist, not a mathematician. This is computer stuff, not maths. Thirdly, it seems pointless at the moment. If it is going to be as accepted as i, [as he's probably hoping] is there anything you can accomplish with it? Does nullility+nullility = 2nullility? Or just nullility? Fourthly, I don't contemplate how he's solved anything, enjoy the person who first came up with i hadn't solved the square root of minus one, he'd just defined it. Nullility is just defining 0/0. Fifthly, this is just an excuse to throw another Greek note into the mix. Sixthly, I accomplish hope they know that if they reclaim that on their GCSE they won't Get anything for it. I hope nobody does worse than they could absorb done because of this. Yours, first-year-maths-student-who-never-considered-Reading.

AhmedThe problem is not the outcome of the zero division but how the computer/device has arrived to this operation to commence with. If the computer is dividing by zero than an error must absorb already occurred a long time ago. Plus, practically, the value isn't as vital as how this value will be used to seize some action. If I am using the outcome of the operation to adjust the pacemaker's frequency, how is nullity going to be any useful? I am sorry, but I contemplate it's a all load of crap.

your motheri believe i talk for sum mathematicians out there when i sigh *ha - ha* O_° this is more ridiculous than that one guy who claims he reinvented relativity motto accelerate of light is actually zero. i can only pray that this nullity thing IS a joke, unlike the above. peace

Anti-Nullitythat would stand for Everything equals nullity. Because their are infinetly many cases of f(x)/g(x) where x goes to some number it goes to 0/0 and could be anything depending on the limit. Any computer revise program knows how to seize limits. This guy just poisoned the minds of several students.

Anti-Nullitythat would stand for Everything equals nullity. Because their are infinetly many cases of f(x)/g(x) where x goes to some number it goes to 0/0 and could be anything depending on the limit. Any computer revise program knows how to seize limits. This guy just poisoned the minds of several students.

MxFinally, they can divide a number by the number of friends this guy has

Zabuza::SWHWouldn't nothing divided by nothing equal everything? Since nothing times nothing is nothing. Then nothing divided by nothing would be nothing. You can't divide a number by zero because nothing can't fabricate something.

GumbyDivide by 0, I want what hes smokin.

MariusIf "infinity" stands for the fact that there ALWAYS exists a number greater than Y, then X in Y=1/X will NEVER achieve 0, because X can ALWAYS be decreased (if it couldn't be, infinity wouldn't exist). Ergo, what you're trying to designation "nullity" here has never existed and will NEVER exist. Calling "it" (in quotation marks because an "it" would exist) a "number" makes as much sense as non-sense (let's convoke it "non-sensity").

BenPerhaps this incredible solution will allow Kevin Warwick to fabricate his robots actually work!

CAUTION Schoolchildren!!!Dr James Anderson, speack about your theorem in front of mathematicians! CAUTION Schoolchildren

Anti-Nullitythat would stand for Everything equals nullity. Because their are infinetly many cases of f(x)/g(x) where x goes to some number it goes to 0/0 and could be anything depending on the limit. Any computer revise program knows how to seize limits. This guy just poisoned the minds of several students.

math_and_computer_guyHere are some facts. You can express infinity and -infinity if your computer uses IEEE floating point arithmatic. Most modern computers do. 1/0 is infinity, -1/0 is -infinity. Both are well defined. Infinity is not the largest number, Infinity*infinity is larger than infinity. Infinity*infinity*infinity is larger than infinity*infinity, ... In IEEE floating point arithmatic, Nan (not a number) is used when the reply is undefined (e.g. 0/0, Inf*0, ...). IEEE arithmatic has both +Nan and -Nan. For example: +0.0/+0.0 --> +Nan but -0.0/+0.0 --> -Nan. 0/0 has an reply they just don't generally know what it is. Sir Isaac Newton's showed us a routine of obtaining the reply if they know how the two quantities involved in the division approached zero.

Mr Sven PerssonWhen i divide by zero on my Mac the calculator says, in swedish, "oändligheten" which means infinity, endlessness. Very beautiful.

Chris HSince this is not a problem in mathematics, my guess would be that the journalist failed to understand what they're doing at Reading. They are probably just using a special value to picture the result of dividing by zero in a computer operation and this is probably a minor variation on the existing special value NaN (Not a Number) used in floating point operations.

domthe Eastern religions got this years ago... its called ZEN

AndyIn reply to PK, nulity is probably any number you want it to equal. I was taught Nuffield Physics and the reply to any problem was some "magical" or should I sigh "natural" co-efficent ie PI = 3.?????

JonathanIt makes sense, but sum he's doing is just calling one thing (an error), something else (nullity), which is not at sum useful in gauge mathematics (nullity is not a number, enjoy pi or i, it's every number simultaneously).

JoshuaI Get it, nothing else for the advice to report on so they hire some guy to fabricate up something lame enjoy this to fill in for vital stuff. Lol.

Doktor ZeroAccording to my calculators 1/1 is "Error" or "Ma Error". Is that the same thing as that eccentric sign? Sounds easier to employ Latin letters... Why didn't he write "Ma Error"?

Jason KerwinThis man is painfully mistaken. Has he ever studied mathematics? I am appalled that he's teaching his kids something a) incorrect and b) that he made up.

DaveComputers are currently able to divide by zero, and the result is NaN. (Not a Number) No crashes, no pacemaker deaths. The traditional divide-by-zero problem is with integers only, and is there for a reason. It speeds up processing if the CPU doesn't absorb to check for that possibility and deal with it. While the nullity may absorb some employ in mathematics (or it may not, for sum I know) I doubt we'll ever contemplate it implemented in hardware.

Oscar Jenkins, UCDHSCIn any field, division by x means multiplication by the multiplicative inverse of x. So if division by 0 is defined, then there exists some number y such that 0 times y = 1. No such number exists in a field. It follows that this fresh structure is not a field, and therefore, fresh axioms for division must be defined for this system to fabricate sense and for the notational manipulations to be well-defined. To wrap it up, you cannot warrant the employ of field axioms if you are not in a field.

By the pass ...1/0 is not infinity; it is undefined. Also, -1/0 is not negative infinity; it is undefined, as well. Any professor of mathematics with a shread of intelligence will relate you that. Furthermore, 0/0 is indeterminate. accomplish you know what indeterminate means? Apparently not. It means it cannot be determined. There is a distinguished contrast between undefined and indeterminate. Mr. Anderson, you should be ashamed of yourself for teaching your flawed "theories" to schoolchildren. I hope the university fires you, and your degree is recinded. Furthermore, this so-called discovery is essentially equivalent to an error trap; something already known to computers and their predecessors, Turing machines.

BradenI guess this is another 'number' for students to drudgery with, such as 'i' (the square root of -1). It will be entertaining to contemplate what they manage to unravel with it.

Alex J.So, they just invented a number and are working to convince us that x/0 is that fresh number? They need an infomercial for this... absorb you ever tried to divide by zero and got an error? absorb one or both of your grandparents died because of this? They can't bring them back to life but... NOW YOU CAN DIVIDE BY ZERO !!! Presenting NULLITY !!! And if you convoke in the next 10 minutes, they might bring back one of your grandparents (we select which one). What are you waiting for, convoke now, now, NOW !!!

BorisOMG YOU CANT DIVIDE BY 0 THIS WILL fabricate THE WORLD retreat ASPLODE!!

So basically ...... your so-called "nullity" lies outside the true and imaginary number lines. If it's not true or imaginary, then what is? (other than totally flawed)

Johnny"Infinity + Negative Infinity. As everyone knows, anything minus itself equals 0" Not anything. Infinity is undefined. What if the positive infinity had greater magnitude? The problem with infinity minus infinity is that it is an indeterminate form. The problem with many of these equations is that they are suppositious to equal infinity, when really they are approaching it. If I were the parent of one of these kids, I would sue the prof for spreading such bullcrap. The issue of division by zero, as well as infinity minus infinity is well solved in Calculus using L'hopitals rule. And as far as pacemakers and airplanes crashing, yeah, it has happened, but I contemplate programmers absorb erudite to entrap the errors now.

Peter FreemanIt will very likely absorb the same impact as the invention of zero (Arabia), a concept that Roman mathematicians did not absorb and limited (along with their difficult numbering system) their mathematical progression. Once the concept of zero in the number system had been symbolized and rules around it were discovered, mathematics went a long pass forward.

Eriki contemplate this is a broad step for the mathamatics history. many problem happens sum the time when diveded withe ziro, many fresh technologies for example. well done Dr anderson. Erik Norway

PeterHaahhaah! The worst thing is I contemplate the guy is serious!! WOW, Reading University seems enjoy a really safe uni!!!!!

DavidHow can they understand his therom if they aren't even told what it is and how to discharge it? sum this guy is even motto is that he made up a number. He essentially pulls math out of nothing! Besides he doesn't absorb a proof for it yet, therefore making uncertian if sum results reached are correct. Even if it does exist and he can accomplish it, and if the "nullity" sits ouside the numberline Computers couldn'tcomprhend it, since they cannot even deal with Imaginary numbers.

Ian LangmoreAre you stupid? Looking over his "axioms" on his website (I can't believe I did this...) you can contemplate that his nullity nonsense is just the extended true line with this added number that comes about whenever you previously tried to accomplish something that would produce an error. His axioms present that once you produce a nullity (i.e. error result) there is no pass to Get rid of it (you can't divide it out or subtract it and fabricate it retreat away). So sum his "results" could be interpreted as: "lets drudgery with the extended reals, then if they Get an error their reply is an error they stop" There would be no reason to continue working since from then on your reply is always nullity.

MARHis theory isn't even a theory. A theory should provide a solution to the problem, rather than introduce more problems. It's just as despicable as those conspiracy theories circulating on the internet.

PeterA lot of people here absorb been making the statement that 1 / 0 = infinity. This is simply not true. It is undefined. Why? because the reply (infinity) does not meet the requirement of division. Normally if you seize the result of a division, the quotient, and then multiply it by the denominator (0 in this case) you Get the numerator (1 in this case). 0 times infinity is not 1. In some special circumstances, infinity is a useful number for 1/0, but not all, and that's why most CPU's absorb a pass to relate the processor to either produce a divide-by-zero exception or to set the result to IEEE-754 infinity.

Rodrigo de Godoy DominguesYes, the concept is quite simple, but more mathematical analysis has to be made in order to proof the validity of his theory. By the way, it was a ingenious idea. Now, hands on... :1)

PhilI guess stupid has no lower limit.

i-AnonSo...this guy gives a designation to something that already has a name, and he gets a advice story? Hey, BBC, can I rename you to UBC and Get a advice legend too? I mean, it's only unprejudiced because you did it for this guy.

Andrew PunchThe crux of the problem with this theory is that it is likely that this fresh representation will absorb exactly the same restrictions as division by zero. The problem with division by zero is that the result is "undefined". Which means that you can't employ it in subsequent calculations. He would need to arrive up with a rigorous proof, similar to the proofs that are involved in complex numbers. And since this is a *maths* problem not a *computer* problem I am very suspicious that this theory comes from a *computer science* researcher.

Jeremy PetzoldCongratulations. I had this thought during my number Theory for my undergrad but never bothered exploring it beyond writing a short unpublished paper on the conjecture.

Kevin KadiumWhy would you want to devide by zero in the 1st place. contemplate of it logically, Yes it its a math equation, and yes its nice to contemplate of a pass to unravel it. But honestly everyone is right. sum your doing is makeing a error message gyrate into nullity. Thats not solveing the problem thats, just replaceing an error message. as LJL said, "doesn't a number lying OFF the number line violate the axiom of Completeness?" How can you be teaching this? It's Rediculous.

Lee"Nullity" is newspeak for "undefined"

PMwhat problem of dividing by 0? I fail to contemplate how this is any better than taking the circumscribe of a function as a variable in the denomenator approaches 0, after sum 0 is much enjoy infinity, it is not really a number - even if it is able to be used as one - but a concept of none. After sum having 0 apples is really not having any, rather than motto the number of apples I absorb is 0. While common language would allow for such a statement the thought behind it is incomplete. To convoke 0 a number is not nearly as incorrect as calling infinity a number, but it certainly is not as accurate as motto 1. of course that actually equals 0.999999999... :D

TimothyHe really hasn't solved anything. Division is always reversed by multiplication. For instance, 4 divided by 2 equals 2. And 2 times 2 equals 4. However, If you divide 4 by 0 and the reply is "nullity", then that means you could multiply "nullity" times zero and Get 4. Impossible.

Assumptions for the winso what he just proved is if they absorb an unsolvable problem, sum they absorb to accomplish is change the designation of something and it's solved?

Dave KornDr. Anderson is nothing but a self-publicist who has made up a fresh designation for something that already exists and is now pretending to absorb invented something new. He has done absolutely nothing of the sort and he has invented nothing. Computers absorb been able to picture one divided by zero for years; they employ the term 'NaN' (stands for Not A Number) to narrate it. motto that 1/0 "sits outside the conventional number line", as he puts it, is exactly the same as motto that it is not a number. This legend should never absorb been published. Journalists are meant to check facts, not just accept whatever they are told by a self-interested third party and publish it without question. Also, someone should relate those poverty-stricken kids that they aren't the first at anything and their teacher has been deliberately misleading them. arrive to contemplate of it, he should probably be struck off for lying to his pupils for the sake of his own personal advantage.

JenUm, no. You can't just fabricate up capricious rules when it comes to math. Did he write a proof?

Mileva MarickSo a fresh sybol solved it all?Interesting...

adelmedicoThere are a few *simple* falsities he writes on his white board. (1) 1 divided be zero is not infinity you cannot sigh 1/0 = infinity. The definition of division is a/b = c if and only if there exists a unique number c such that a = b*c. So by motto 1/0 = infinity, he is claiming that 0*infinity=1, REALLY??!! (2)In his proof when he gets down to (1/0)(0/1) = "nullity" he's forgetting that 1/0 = 1 and according to him, 1/0 = infinity, then that line of his proof reads as 1*infinity = nullity. Silly me, I thought that 1*infinity = infinity!

Bill MerrillThis doesn't appear to be about dividing any number by zero except for the number zero. Therefore, it doesn't unravel anything, unless I'm missing something here. If I commence the problem by asking about the value of 2 raised to zero, following the methods in the video I discontinuance up with it equaling 2/2, or 1. Thus, any number raised to the zero power is one, except zero, which is nullity. Not positive where this gets us....

J. PehkonenYou guys are defining your own mathematical rules for this number, and then disproving his theory by using your own made-up-rules. recollect that in imaginary numbers i^2 = -1. Perhaps nullity besides has its own mathematical rules? The same goes with INF/INF not equaling 1.

KI contemplate nullity is the terminal number in pi!

Scott PerryIf you've ever done any programming, you'll know this is traditional news. Dividing by 0 is something that programs can be written to catch. If they don't, the computer doesnt just die -- the Operating System kills the process that tried to divide by 0. It's not terribly difficult to check your denominators.

HOVISI absorb a problem, I don't know the answer. I contemplate I will just fabricate one up! Hopefully no one will notice if I accomplish lots of workings out to fuddle everyone. The only thing this guy is teaching is how to be creative. Some thing maths is not. Obviously he is not a true mathematician!

Luke WhitingAny programmer worth his salt wouldn't allow a divide by zero to occour in the first place! It's never been true problem in modern programming. I contemplate this is sum a bit silly. "I know. Lets fix a problem by adding a fresh number to the world".

TomWhen computers divide by zero, they continue working. x/0 = DivideByZeroException. It's called error handling and unless you are one of those idiots writing } entrap (DivideByZeroException dbze) { // DO_NOTHING } you will never absorb a problem

David TurnerTo sum you people who talk about diving cakes between people... Divinding isn't about how much is left once you've handed out the pieces of cake... Trying to apply division to cake, you don't sigh "How much is left after giving this to X people", you sigh "How much does each person get"... So the division-by-zero problem in cake terms would be "If you divide this cake between no people, how much cake does each person get". At first Nullity sounded enjoy a safe idea, but it's not really a solution, just renaming the problem, as others absorb stated.

AnonI hope someone is going to re-educate these poverty-stricken children afterwards. The BBC should be ashamed of themselves for publishing this.

Baron von MannsechsGood job Ranjit--confuse Science vs. Engineering.

Jake Haseman...Infinity anybody?

Question Dr. Anderson?"...It is just an arithmetical fact that 1/0 is the biggest number there is.... " --- If 1/0 (infinity) is the biggest number there is... then is .5/0 or 2/0 twice and half as large? --- Does a number half of infinity divided by infinity prove 2=1? --- Why accomplish existing rules about treating non-numbers outside the number line not apply here?

AnonMy pacemaker divided by zero and nullity happened.

GeorgeI abominate it when my bike divides by zero and the brakes desist working.

John GoodHow is the definition of Nullity different from that of Infinity? Or for that matter "Undefined", which some calculators will spit out if you try it. I've got a better designation for it: BS

NanThis is some kindhearted of joke, right?

Matze M.I prodigy how long it takes until somebody tells them that at the very position where they placed this "nullity" is already (0 - 1*i). But until then, it's quite worth a laugh. Thanks, man. Made this day a droll one.

BobWill this antecedent Bill Maher to abominate and deride practicing Christians, and Catholics in particular, any less?

brynjolfTHis is compleetly wrong. a^0=1 Therefore Nullity = 1

Mathiasok.. this kinda makes sense, but what about infinty divided by infinity? Is that 1? I tried to employ my texas instruments calucator but it just shows an error...

GnomeStep 1. Create solution 2. Create problem 3. PROFIT!

The fresh Mathturns out nullity is besides the terminal decimal digit in pi.

Desperately Seeking SenseI Get it. I don't know if it's terribly useful, but I Get it. If zero is enjoy a void, then nullity is enjoy an endless table with void cells. However, once you apply a value to it, it becomes illimitable by any means, therefore becoming infinity. (unless you can have: [infinity] * 2 ) Maybe that's for Dr. Anderson to figure out next year. I adore imaginary numbers; they're enjoy imaginary friends you can participate with really smart people.

Daniel AsimovI am a mathematician. Mathematicians absorb been gracefully dealing with division by 0 for millennia. It shows the massive incompetence of the BBC advice Division that it would not absorb occurred to them to check with a mathematician before turning this report into a advice broadcast.

Ramesh ArakoniWhy accomplish you waste your time (and mine) publishing such rubbish.. btw.. what they enjoy to convoke NaN (not a number) has been given a fresh designation and oh.. nullity/nullity= insanity :)

Leo CIt's nonsense my dear dr. Anderson. You've solved nothing with this theory.

JustinWay to go, you renamed the error message. You soundless don't understand the nature of infinity, or as you absorb now decided to convoke it, "nullity." From what I've read, nullity encompases positive infinity through zero through negative infinity, which could besides be refered to as INFINITY. You just called it by a different name, you didn't unravel anything.

CS grad studentHoly cow! From what school and department did this guy Get his PhD? Such bravado and immodesty - Unbelievable. It makes me respect true mathematicians even more.

HamidI believe that the problem is soundless not solved, because Dr Anderson considers that zero over zero is equal with zero (0/0=0) and he replaced zero with 0/0 in beginning. The fact is that 0/0 is unknown, and it doesn’t absorb any specified answer, zero is just one reply of many answers to this devision (0/0), this is in contradiction with a simple division enjoy 18/2=9, because in ordinary divisions you Get a specified answer. The problem with “nothing” will never unravel because “nothing” is an agreement.

MattWhy did you designation undefined?

Richard C. MonglerI divided by zero and the universe imploded.

stupiditus stupidensisJust plain stupid. I prodigy where he got his diploma...

Leo CIt's nonsense my dear dr. Anderson. You've solved nothing with this theory.

AnonSorry guys, this thread fails. There already is a symbol for 0/0. It's "O SHI-"

Ian BennettNull is hardly a fresh concept. Databases has been handling the concept for years; a field which has had no value entered, not even a zero-length string, is 'null'. A null field has no length, not even zero. It's safe that children are being exposed to the concept.

scottoSo you can unravel a math problem by making up a symbol? Wow.

JCI adore the pass sum of these 'non-mathematicians' employ arguments enjoy "If I divide a pizza among 0 people I haven't done anything to the pizza so I absorb one pizza." To present why it's wrong, you need to realize that the question is wrong. It should be more enjoy this: If I divide a pizza amongst 5 people, how much did each person get? A fifth of a pizza. If I divide a pizza amongst one person, how much did that get? One pizza. And then you can contemplate logically why you can't divide things by zero normally. If I absorb one pizza and divide it amongst 0 people, how much did each person get? It can't be zero pizza, that would imply there were people to Get one pizza. It can't be one pizza either, because nobody is getting a all pizza. What Dr Anderson says is that if I divide one pizza amongst zero people, those zero people are getting illimitable pizzas! It's laughable.

FrostyI contemplate this could absorb safe employ as a backup if electronics or computer accidentally divide by 0, but other than that I don't contemplate any true use.

HKewwww, that's disgusting. Seriously, you really shouldn't train students anything that doesn't absorb a solid scientific background. It'd be enjoy ... teaching creationism.

JImmy RuskaDivision is a function intended to rupture an input equally into a set number of pieces. Without giving a sound number of pieces you want your input to be equally divided into, you are invalidating the purpose of the function known as division. Replacing an unworkable or unknown value temporarily with a note is not something novel. There's no need to super impose an I over the 0 to be fancy. I can't contemplate how this is a novel idea, and I can wager any efforts on algebraic simplification has been well exhausted.

don't really need to knowdude.. he just took out a 1200 equation by making 0 devide by 1 b4 he applied powers? the number 1 rocks lol btw thx mate u just took down the all of calculus! btw anynumber devided by 0 is either a: not possible, b 1, c 0, d the number itself, e infinity- gratify fabricate this a vote bbc!

JCAHas anybody an insight into what rank the zahlenkoerper of Dr. Adersons's findings has?

Erik Schaefer, Madison, WII hope this gets world-wide acceptance because I want to be the first person to absorb the moniker of the only man in Wisconsin who has had sex "nullity" times.

fffomg nothing is nothing???? humor = BLOWN

ReidA proof of the mathematical inconsistency of this construction. First we'll seize what he has written about the true number line. Namely, the reals are the rational and irrational numbers. Then they add in +/- infinity to Get the extended true numbers. He then writes infinity to be 1/0. This is sum they need to present that there is a mathematical inconsistency which they accomplish presently. Now, since infinity now can be expressed as a rational, it is an element of the rationals. Since the rationals are a subset of the reals, infinity is an element of the true number system and thus is an element of the extended true number system. Thus, they absorb a contradiction because infinity is defined to be both internal and external to the true number system. QED

Anonymouscannot divide by zero world will explode they are brainwashing kids to blow up the world by doing 'math'

/b/The discontinuance of the world is here.

Jordan LundCreating a fresh imaginary number doesn't unravel the problem, sum it does is apportion the problem an imaginary status.

how embarrasingWhat can they in gyrate learn from sum of this? Avoid embarrasing yourself on an international scale by taking 10 minutes to retreat down the hall and check with the math department to fabricate positive your ideas arnt stupid. He could absorb at least reclaim his ideas up to peer review before forcing it on his students and parading it around as mathmatical fact.

Dr Sanford GraceThis man is a blithering idiot!

Ned PetersTell me this is satire. Please, gratify relate me this is satire. If it isn't, then whoever wrote this article should be fired and and not allowed back into the press until he sucesfully completes a lofty school mathematics course. Or a middle school one, for that matter.

Magnus MaximusHumankind introduced zero in the 15th century, which was considered definitive step in sciense. Now, why does humankind bounce zero? Just to reinvent it in 1200 years??

SteveThis nullity thought is meaningless. He hasn't shown why it's useful. Also, it has been agreed that x/0 = +infinity, where x is any number between -infinity and +infinity, so his proof is pitiful and hasn't solved anything. In fact, he has just re-iterated something that has been known for a long time, so giving this solution a different symbol means nothing

PatrickIf I were to absorb a forumula that had somewhere along the lines an X that is 7/0 and later absorb X*0, the /0 and *0 would cancel each other out and I'd Get my number back. But if I evaluate 7/0 to Nullity, and then multiply it by zero, my number is gone.

Stay at home momRenaming the problem is NOT a solution. The guy is a total dingbat.

benjit's difficult enough with 10 numbers to recollect I DONT WANNA recollect ANOTHER NUMBER

AhmedYou absorb got to be kidding me. Looking forward to seeing Reading University maths application plummit.

nullFunniest BBC article ever. I hope this guy has a lot of savings so he can retire to an island somewhere.

asdfdivision is basically subtraction. For example: 4/2 means how many times can you subtract 2 from 4, in this case 4-2=2, 2-2=0 (so the reply is 2). Now if they examine at division by zero, for illustration 4/0, this is basically asking how many times can I subtract zero from 4? The reply is: 4-0=4,4-0=4,4-0=4,4-0=4 .... This goes on forever, it does not discontinuance .. meaning its infinity it is not the largest number possible. In fact there is no largest number. Lets sigh x = the largest number possible, then what is x+1? As for 0/0, it should equal one. Because it asks how many times can you seize 0 away from 0, 0-0 = 0 (that's 1 times)

ClemensOkay, but how accomplish you want to dividied the fresh number? I think, then there is the same problem again...

RudnickiIf anyone with any mathematical background was asked to evaluate the expression x/x, they would sigh that x/x=1. EOF.

The Nutty ProfessorIf I absorb 2 marbles and I divide it over 0 persons then I haven't lost my marbles, right? I soundless have'm. But according to mathemagicians I discontinuance up with nullity and loose my marbles?

Dr. Andrea ArmaniMark Skerritt answered this problem (along with sum of the people who proved this proof was incorrect) - employ Calculus. If this guy is a Dr. in a comp sci department, he should absorb taken calc. and this is the first problem that is addressed in any calc course - solving 0/0 using summation. On a side note, Newton developed Calculus. So yes, Newton solved this problem. I don't know who the other two doctors are who vetted this proof, but they didn't accomplish a very safe job.

EmanuelThis makes me laugh . did he accomplish this for present !? " it's that easy" ...

take a pissSo what is 10/0? How accomplish you approach nullity? does nullity arrive before zero?

Bob"I wrote the all lot down as analytic rules or axioms. Dr. Andrew Adams from Reading University and Dr Norbert Voelker from Essex University helped me develop the axioms. Norbert translated the axioms into higher order logic and used a computer to prove that they are consistent." Both of these people are computer science "Dr.'s." Just because you can write your axioms in Prolog doesn't stand for it doesn't contradict everything they already know about mathematics. Try lambda calculus.

Josh JelinDr. Anderson doesn't really know what he's talking about. Defining a number as the solution to a problem doesn't unravel the problem. Mathematicians thought of his solution hundreds of years ago but instead chose to leave 0/0 undefined because “nullity” is useless. This would be exactly the same dispute as motto they “solved” the square root of -1 by renaming it to i.

KainawYes - I understood it back in 1978 when my geometry teacher explained that it was used to create the Cartesian Graph (the Y-axis is div0 - a line from negative infinity to positive infinity).

ComputerManThe international gauge IEEE 754 defines representations for Infinities and for NaNs (Not A Number)s which accomodate Dr. Anderson's theory. So what's new? Computers may crash if they haven't been programmed to allow for these exceptions to the norm (and not many accomplish in my experience) but they could do.

khris777I wouldnt view 1st alien contact if i had to employ true player to contemplate it.

Burt WurstheimerThe wurster says: Stupillity. Reduntillity.

FrankIf you would enjoy to accomplish an article on me, I besides figured out a novel problem.. Using the same logic, and inspired by Dr. Anderson. The solution to gelid fusion. It's easy! See, E=mc^2. so mass can be converted to energy. To accomplish this, you need specific conditions for the reaction to happen. I absorb arrive up with a fresh term "energity". by adding mass + energity = electrical energy! Not only does it produce energy, but it is electrical energy rather than heat and electromagnetic radiation. This means no conversion is required, you just seize some material (garbage for instance) and add energity, and you Get electrical energy. pretty simple huh? Better yet, computers can easily unravel the equation without displaying an error message.

ChrisMathematicians absorb been "joining" the ends of the number line with a "point at infinity" for years. It's an vital fraction of the theory of elliptic cryptography. This is nothing fresh - just a coat of whitewash and a different designation over an existing idea.

A. SupporterI know nothing about this

dave pIf Dr Anderson insists on putting nullity there, then there is no latitude for i. Cancel that complex Analysis class matron.

Non ScientistAll this mathematics stuff is great, just a shame most cannot spell. Now there is a 'real' problem.

ChristieMajor Flaw in his "problem solving"...he is applying the rules of the true numbers to a set that is "outside of the true numbers". x^0 = 1 in THE true NUMBERS since nullity is NOT A true NUMBER you cannot apply the same rules!!

IanSo could the professor gratify explain the properties of nulity under addition, subtraction etc...sounds enjoy the "bottom" value from lattice theory to me ... but that's nothing new. Next week, Reading Uni discovers set theory

Craig BruceThis sounds a lot enjoy what is implemented in IEEE floating-point numbers (which are used on sum modern computers), except that it gives "nullity" the designation "NaN" for "Not a Number". NaN operates basically enjoy a trap in that any operation involving NaN will produce NaN as a result. Of course, I don't really contemplate how you withhold airplanes flying when every flight-control calculation results in NaN or "nullity".

StuartZero divided by zero has always been defined as zero. A-level maths. The fact that computer's processing microcode doesn't handle division by zero is irrelevant. Everyone checks for zero in their code and avoids it. Computer Science O Level. So - this astounding revelation is impertinent to any one with a qualify education. Well done the BBC - absorb zilch of you got any Science qualifications?

Nullity MasterBS Theory Divided by the 0 number of people who are digging this legend equals the nullity casual anyone will ever seize this Dr seriously again.

PythagorasWho is this guy who says I can't unravel problems? Heck, I've been dead for more than 2500 years, so where does the 1200 years arrive in? retreat meet my mate Giuseppe Peano who first wrote down the basic axioms of arithmetic. He'll relate you whether there's a Nullity or not!

nitroxDefine nullity as 42 and you absorb got the reply to sum your x/0 questions :-)

alexthis is retarded... i've been setting nulls for years when division is by zero... how does this equate to solving a problem?

PeteDr. Anderson: I'm confused as to why you can rewrite 0^0 as 0^(1-1) (or why you can even write 0^0 at all) from your list of axioms. Could you rewrite this proof without any shortcuts and annotate each line with the axiom used from www.bookofparagon.com/Mathematics/PerspexMachineVIII.pdf?

jack welchI contemplate he may be on the verge of greatness! Nobel prize?

GWBIt's MMD!!! Mathematics of Mass Destruction. They must now dispatch in the troops.

DBI conform with PK and similar responses. For some 60 years I absorb always understood that 0/0 is any number. 'Nullity' simply means any number. I would adore to contemplate any application of the concept of nullity. The children must be very confused.

just some professor of physicsIsn't it obvious - this guy is a lunatic. If he really had something new, he would be publishing it in a peer-reviewed mathematical journal rather than trying to peddle it to children. My god, are people so gullible. I guess some are, because after sum Reading University hired him, the BBC reclaim him on the news, and the school at Highdown let him train their students.

NostradamusI told you this day would come.

KarlDr. Anderson should read "Nonstandard Analysis" by Abraham Robinson. Robinson came up with a consistent algebra that employed classes of infinitesimal and illimitable quantities about 50 years ago. Using that algebra he showed he could create the same calculus they sum know and love, but without using limits.

SekkyThis man is a computer scientist, not a mathematician. I can't believe these kids are buying into to this garbage. I besides can't believe that this man can believe that nobody else has ever thought up of giving a fresh damn designation to an already existing concept, especially considering how NaN already exists and he is, supposedly, a Doctor of computer science. NaN works well, this is simply a stupid relabelling. Of course you've 'solved' it, you defined it that pass in the first place! I dare him to dispatch his into MIT, Cambridge or Clay, they'll shoot him down in seconds. BBC you should be ashamed to absorb featured this, unhurried day for advice was it?

Cameron Kenneth KnightAlthough I accomplish not believe that Dr. Anderson's theory holds water, to the people who request to present the number in binary really need to study the IEEE-754 standard. The IEEE-754 gauge specifies binary representations to 32, 64, 43, and 79-bit floating-point numbers. In this spec allows for the numbers infinity, -infinity, and NaN. Since NaN is essentially what Dr. Anderson descibes as nullity, one could employ that as its repesentation. Also, NaN is defined when the exponent is 2^e − 1 and the mantissa is non-zero, which covers many, many numbers. One could instead define NaN to be where the mantissa is non-zero, non-1 and nullity to be where mantissa is 1. Integer representation of nullity (and besides infinity and -infinity) is typically not needed, although if you were to employ a modified integer set, it could be done. E.g. looking at an 8-bit integer typically defined as -128 to 127, one could define 127 as infinity, -127 as -infinity, and -128 as nullity.

p@Some of the people bashing this should learn some basic maths. Others should read the papers he has written. soundless others should learn to read the first line of the article above, which is fairly limpid that Dr Andersen works at a university, and not a school. Unfortunately the ill-informed comments so outweigh any useful criticism it is difficult to find genuine, sensible, objections. Those with sensible objections would probably be most welcome to hunt down Dr Andersen's email and present them to him - so far zilch of the mathematicians who absorb tried absorb managed to present there is anything wrong with transreal mathematics (well... I pointed out that his earlier version was lacking negative infinity) The comments about NaN often fuddle infinity with what Dr Andersen is calling nullity. Some programming languages define infinities as well, however, and from this perspective I believe some of the criticisms are valid.

KnightRiderIs he suggesting that coconuts migrate?

Math GuySad reflection on the situation of scientific erudition in journalism (which seems to be closer to zero than to nullity ;-). Why even convoke attention to this vapid, void theory (not to mention the preposterous claims that the problem was 'unsolved'). If anything, the problem was ignored, because it is of no significance. Shame on you BBC.

Mark Wagner"Nullity" is hardly a fresh concept in computing. The IEEE gauge for computer mathematics defines three "non-numbers" that can result from an operation: positive infinity (the tangent of 90 degrees, or 1/0, or any of a number of other operations), negative infinity (the tangent of -90 degrees, or -1/0, or any of a number of other operations), and not a number (0/0, or infinity/0, or -infinity/0, or other operations that are not well-defined). Calculus-level mathematics has been able to deal with 0/0 for a shrimp over three hundred years. It sum depends on where the zeroes arrive from: 0/0 could be 0, or 17, or any other number. There's a technique called L'Hopital's rule for determining this.

SpicemakerMany of the operations Dr. Anderson performs to "prove" this (such as the algebraic principle that (a/b)^{-1} = (b/a) ) _assume_ the basic field axioms. Of course, these axioms assume that aa^{-1} = 1 only if a ≠ 0. Dr. Anderson first has to present that if you extend the field axioms to involve 0^{-1}, then the habitual algebra applies to it. And he hasn't.

JBSee www.jamesanderson.co.uk for James Anderson the estate agent (top of the list under Google). Now sum becomes clear!

DanMahesh Sooriarachchi, what you propound is (an apple)/0 = (an apple) which means basically that 0 = 1. Which better not be the case. dividing by 0 cannot exist or math doesnt work.

Ashley ColeI am currently studying mathematics at A level, and this cannot be real. Surely he cannot jsut fabricate up a fresh number? If anything it should be under imaginary numbers? I disagree with what Dr James Anderson has proposed, as you cannot divide any number by zero, as there is nothing there to be divided by! It cannot be done.

terrySo he worked out that the zero to the power of zero was zero and gave it a name?

John MeagherDr Anderson may absorb the birthright idea, but the naming convention is a shrimp off. According to Dr. Anderson, when you divide by zero, your reply goes to infinity (+/-), and covers a ambit of numbers starting with the next number beyond the numerator to infinity. However, "nullity" indicates a NOT anything, even though dividing by 0 is a NOT NULL answer. I'm not a math wiz, but it would fabricate sense to me if dividing by zero is soundless a controversy, then "nullity" would be a "not defined". By placing "nullity" outside of the number line, indicates the reply is soundless unknown. If the reply is unknown, then "nullity", with sum that the designation implies would be an inappropriate name. "nullity" would be appropriate, if the influence of dividing by zero results in zero (null). This tends to fabricate more sense to me: 0 x 5 = 0 0/0 x 5/0 = 0/0 5/0 = (0/0) / (0/0) 5/0 = 0 If 0 follows the conduct of little numbers, then the reply is infinity. If 0 is treated as null, then dividing by null is the same as dividing by 1; No influence on numerator as a given number over one. In either of these cases, "nullity" is not an appropriate designation for a not-null result.

Chuck NorrisOnly Chuck Norris could divide by zero. And I've done it twice.

HihoWhat a bunch of baloney! The problem with 0/0 and 0^0 is one of uniqueness, not of simply needing a designation for them.

jbuddenhmy digital camera tries to divide by zero quite often, i absorb to seize the battery out and reinsert it as a workaround. dr anderson's simpler solution would reclaim me that trouble! he should let nikon know quickly!

Ex of ReadingMessage for Kevin Warwick: be afraid, be very afraid!

HenryThe problem is that dividing by zero is not a problem. It's not an operation, just as jumping without lifting your feet off the ground is not jumping, or eating without opening your mouth is not eating.

StephenThis is total crap. Of course the students are confused. It's entirely wrong! I can construct a vast number of examples where 0^0 is one, or zero, or one half, or a variety of other values. Can I compute something with this "nullity"? I contemplate not. 0/0 is an undefined form, and there are an illimitable number of workable values for it. This is nothing but some computer science PhD delving into the world of number theory when he really shouldn't, and sum it is going to accomplish is fuddle the students he teaches, especially when they Get to a true maths class.

NuriThe true Numbers shape a complete ordered field. Let's just examine at how well Nullity fits into the true Field. field INCONSISTENCY The true Numbers shape a field. In it, every number except the additive/multiplicitive identity has a unique sunder inverse element such that x*x`=E. What is nullity's inverse? Let's examine at the multiplicitive inverse. Nullity's multiplicitive inverse would be 0/0 (it's reciprocal). By this result, either E=Nullity=0 or Nullity is not in the set of true Numbers. If it is not in the set of true Numbers, what set, group, ring, field, algebra does Nullity felicitous into? Would 10 Years kids be able to grasp a sunder set of rules sunder from the rules they've erudite thusfar? There's a reason this professor is teaching lofty school children... That reason is not flattering.

my nameand the square root of -1? i'll convoke it bob! it lies off the numberline, and i've just solved an age-old problem. want to link the problem-solving fun? just rename everything! it's easy!

PeteHow about encoding the video in a format that's not as worthless a $0/0... MPEG is an industry standard.

EisenfostThe next mask for 1/0, after Nullity, shall be Willy-Nilly!

Flash Cutnullity =NaN(Not a Number) accomplish you contemplate people are stupied???????????? Try again .LOL

Percival SittingbourneThat's Numberwang!

ArturitoUhhh, Riemann Sphere? This guy is 150 yrs slow.

O RamonIf you absorb nullity over nullity, does this stand for that it is equal to 1? or would it remain outside the number series. If you multiply nullity by any true number is it soundless a true number, or is it nullity? If you multiply a nullity by an imaginary number, it it in either or both sets?

MaczComputers absorb this concept already. It is called NaN. This guy should not be allowed to teach. His axioms=diddly/squat.

Eric (M.S. Mathematics)I had an uncle who was a philosophy profressor (now deceased). For entertainment, he used to affirm that there was an extra integer somewhere between 8 and 9. He'd relate everyone he was working on a proof named "the sneak" whereby he planned to line up 10 oranges and then, somehow, "sneak" the extra orange somewhere between the 8th and 9th one, thus proving there is an extra integer in there somewhere. He'd relate people about this and laugh until he had tears in eyes. Yet, somehow, his mathematics are more appealing to me than Dr. Anderson's. At least they're funny.

coyotethis is not a significant 'discovery' and should be peer-reviewed. his derivation [shown in video] contains two potential meanings for 1/0. the first is his infinity. the second is to ignore it while doing his 'solution', he says that 0/1 x 1/0 = nullity... this is abstruse given his prior definition of infinity being 1/0. now, infinity multiplied by zero is nullity. on a side note. i would enjoy to contemplate his version of common algebra using nullity. 37/0 for instance. 37/0 = 37/1 x 1/0 = 37 x infinity ... but 37/0 is 1/0 x 0/1 x 37... this seems to be not clearly defined in terms of behavior. this seems problematic as they are now back to the original division by zero being undefined if multiplication is not consistent.

Erik MesoyThis has more holes in than Swiss cheese. By his math, 1 = 1/1 = (1/0)*(0/1) = (1/1)*(0/0) = 1*Nullity. Hence nullity must be the multiplicative identity element, nullity=1. I besides note that this is filed under "people" not "science", and the man does not absorb a math degree but a comp sci degree. Another hole: (a/b)/(c/d) = (ad)/(bc), so (0/0)/(0/0) = (0*0)/(0*0), and thereby nullity/nullity = nullity. Divide by nullity on either side and you Get nullity=1, multiply by nullity on either side and you Get nullity=nullity^2. Also, this breaks mathematical groups and rings too. 1+nullity=? 1*nullity=? 0*nullity=?

PWebinfinity/infinity is not equal to 1 any more than infinity-infinity=0 . Infinity cannot be treated enjoy a regular number. Just because they don't know what nullity/nullity is doesn't stand for the thought is pointless. Let the scientific community sort it out before you sum grimy your pants in frustration.

Disgusted in VegasHe's actually teaching this to students as legitimate "mathematics"?

ZenoThis is a load of crap. motto dividing by zero results in something that is not a number (nullity) solves nothing and breaks mathematical closure. It is shameful that this idiot is allowed to screw sum those kids up. If he has a degree in mathematics it should be immediately revoked, as well as his teaching credentials.

Free Will ::= NullityIn his works, Mr. Anderson proposes that a "free will enjoy ours" does actually exist. If so, then nullity actually does exist. However, both are just artificially making up something that is actually undefined. No problem solved, only postponed to a future representing some instance of nullity.

Nick WilsonWhat 'problem' is caused by division by nought being undefined? How does this aid anything in any way? You can trivially define it any pass you like, but so what? This causes broad problems - his axioms must be a total rewriting of sum their basic arithmetic. This is very stupid. PS lots of people appear to contemplate (oddly) that 1/0 = infinity -- THIS IS NOT TRUE. 1/0 != infinity. It is undefined. lim_{x \rightarrow 0} =\infinity (in words: the circumscribe of 1/x as x tends to 0 is "infinity", but has NO VALUE at x=0) They employ a lot of different ideas when they talk about "infinity". The calculus thought of an arbitrarily large number (ie 'limit as x tends to infity' or '1/x tends to infinty as x tends to 0') is different from the thought of, for the instance, the number line being "infinite". The transfinite numbers (\aleph_{0}, etc...) are yet another different meaning of the word infinity. Did this idiot Get his Doctorate in Geography or something? I can't believe no-one has told him that throwing an exception on division by zero is safe - would they rather absorb the plane plough into the ground because it ignores the error? Catching exceptions is safe software design, not ignoring the problem by renaming it.

jhughsResponding to "Pythagoras'" question about whether or not 2/0 is twice as illimitable as 1/0. Although I don't know exactly if that's correct, it is mathematically revise to sigh that some illimitable sets are larger than others. respect the following three sets of integers: a) 0 to +infinity; b) 0 to -infinity; and c) -infinity to +infinity. If you contemplate of it in terms of the lines growing away from 0 then it's limpid that set "c" is twice as broad as either set "a" or "b". An even more unsettling illustration is the set of integers from 0 to +infinity versus true numbers between 0 and 1. If the first set grows at the rate of 1 integer at a time, but the true number set grows by halves (ie, 0 & 1, 0 .5 1, 0 .25 .5 .75 1, etc.) then the set of true numbers not only grows faster than the integers but it grows infinitely faster. And so, it is a fact that some illimitable sets are larger than others. I know, it threw me off at first too, but now it seems reasonable (which is safe or I would absorb failed the class where they erudite that - although now it only comes in handy for showing off).

Captain AnonInsanity! 1/2 is equivalent to 1*(1/2) 2/2 is equivalent to 2*(1/2) 0/2 is equivalent to 0*(1/2) Now m/n is equivalent to m*(1/n) 0/0 is equivalent to 0*(1/0) Everyone knows 0 * (anything) is 0. So, "anything" includes sum numbers, true and imaginary. a. 1/0 = infinity b. 0*(1/0) = 0*infinity c. 0*inifity = 0 Hello?

MOVThat makes no sense at all. 0^0 is not defined, therefore 0/0 is not defined. You can't prove anything by confusing people with wrong facts.

ZenaMakes calculus a all lot easier too. lim(x->0) x/sin(x) = 0/0 = NULLITY!! Oops. Looks enjoy we'll absorb to rewrite sum the math books in the past 500 years.

Wlymsksprmuch ado about nothing

Egon IpseThis is funny! To sum people posting here: YHBT. YL. HAND! Just examine at his grin on the video when he claims that the reciprocal or 0 is 1.

RamanujanI hope Dr Anderson gets a huge monetary prize for his discovery so he can retire and desist teaching children. What a shame, where this world is going...

Anony!OK he's just a very newb at comp-sci math professor who thought he came up with something original. I'd wager it wasn't his thought to retreat to the media, though. Computers CAN picture -/+ infinity, and often do. Also, what is infinity * 0? ZERO. That's why dividing by zero makes no sense, since division is the analytic converse to multiplication. The problem this article raises is exactly what kindhearted of crap their school systems can shouvel to kids. I am not religous, but I was taught at school that evolution was "THE WAY" even though it's just a THEORY, and I'm pretty darn positive that's not how honest scientists would want it.

RPGreat. This guy has spent sum his time coming up with another symbol for infinity. I could produce an equally useless symbol, oneity, for the result of a number divided by itself. Is that groundbreaking? However, I suppose it does account for sum those times planes absorb dropped out of the air. It wasn't lofty turbulence or some sort of storm. The plane simply tried to divide by zero.

Steve Q.All maths problems are easily solved if one wishes to simply fabricate up a fresh character to status on the birthright hand side.

ChrisSo, relate us more numbers on this fresh number line, sir! You've given us a number that can be any other number (as where x is any number x*0=0, so 0/0=x, which means nullity=any number). How about a number that can accomplish backflips? Or a number that can gyrate invisible?

SumDude"which solves maths problems neither Newton nor Pythagoras could conquer" How ridiculous! The reason neither Newton nor Pythagoras "conquered" this problem is because is because it has already been solved. 0/0 is undefined and calling it nullity does not change anything. How does this "new" theory of his provide a fresh reply for 5 * (0 / 0)? The only change now is that instead of getting "division by zero" computer exceptions one would Get "arithmetic involving nullity" exception.

CarlosThere already is a designation for this number: QNAN Nullity is just a despicable designation that implies the antithetical of what it is. A better designation would be inverse nullity.

What happens when you assume...First of all, don't trust a mathematician who issues erroneous statements. 1/0 is not equal to infinity; similarly -1/0 is not equal to negative infinity. If they want to compute 1/0, they accomplish this by taking the circumscribe of 1/x as x approaches 0. So let x = 1, 1/2, 1/5, 1/10,000,... Clearly 1/x gets inifinitely large as x approaches 0. But what if they approach 0 from the other side (the left limit)? When you let x = -1, -1/2, -1/5, -1/10,000,..., then the circumscribe of 1/0 approaches negative infinity. Since the left circumscribe and birthright circumscribe of 1/x as x approaches 0 accomplish not agree, they cannot sigh that 1/0 equals anything. (Want to picture it? A similar illustration would be the graph of the tangent function. relate me what the circumscribe of tan(x) is at pi/2 radians, or 90 degrees.)

EdwinI invented the number 5. People appear to enjoy it.

J. A. O. EkbergThe problem with this is not that it's wrong or useless (it's not). It's just that though I absorb never seen formal proof of it before, nobody ever severely doubted that arithmetics including +infty, -infty and "indeterminate" can be axiomatized. Talking about such things at schools is not a despicable idea; renaming "indeterminate" into "nullity" and claiming this is something revolutionizing is quite another thing. In terms of novelty (though not usefulness, perhaps), Jesper Carlström's wheel theory is much more interesting.

Ron LarhamComputers can divide by zero if the arithmetic is implemented correctly, 0/0=nan, 1/0=inf, ... by the pass nan means not-a-number.

Jim BelcherThis is too much of a abstract abstraction. The proof of its validity is likely to equivocate in finding a practical physical application. Mathematicians are know for abstract ideas that are proovable only on the blackboard. OK, so they can accomplish it on paper, so what?

cwm9Every mathematically inclined person is probably groaning birthright about now. This is utter nonsense. The theories of 0/0 absorb been worked out for ages -- there's no mystery here. You can't know anything about 0/0, you can only sigh something about the circumscribe as you approach this situation from along a continuous line. retreat examine up L'Hopital's rule. You can't even sigh infinity"nullity. Heck, you can't even sigh infinity=infinity. There are different classes of infinity. About the only meaning "nullity" could absorb that would be reasonable is "undefined." Which, OMG, has already been used to define this state. About the most he could be credited for is inventing a fresh symbol for the word "undefined". Utter rubbish.

NicholasThis guy is just assigning a symbol to something that soundless isn't a number. It's enjoy me renaming the Sasquatch a "writing desk", pointing to a desk, and claiming that it's proof that the Sasquatch exists.

Adam Setzler1/0 = Infinity 23/0 = Infinity 37/0 = Infinity 419/0 = Infinity 2305/0 = Infinity 12904/0 = Infinity 349002/0 = Infinity . . . Infinity/0 = Infinity Infinity = Infinity Your mom.

Cambridge Maths PhDHaving just read his papers, (and as other people absorb suggested) the symbol Phi is nothing more than a shorthand for "undefined". He lists his axioms which are easily understood with this understanding. This really is a second-rate piece of work. FORTRAN already uses the system he is advocating (Phi=NaN).

DavisHint to the BBC -- talk to an actual mathematician before publishing such a dreadful piece. We're really quite approachable, and perfectly delighted to explain why this is silly.

RayDr. Anderson obviously knows nothing of modern algebra. There is a very concrete reason why division by 0 is impossible, and if he wishes to fabricate it workable he must besides be willing to find a replacement for the foundations of much of mathematics. The true number line is a field, and it is not workable to absorb division by zero, the additive identity, in a nontrivial field. You can't just fabricate up a fresh symbol and discharge a handful of mindless operations on it to unravel a "1200-year traditional problem". If he wishes to be taken seriously in the realm of mathematics, he must provide a radically fresh algebraic structure within which his nullity may exist. I don't title that such a masterstroke is impossible, but until it is accomplished, his "result" is illogical and should be labeled as pseudomath.

MikeThis is a safe lesson for sum who listens to "scientists" who preach global warming... Thanks professor

AnonThis is absolute crap. Who hasn't thought about replacing the concept of division by zero with some symbol while they were learning about replacing the square root of negative one with i? If this is a breakthrough, I should seize over this guy's job. At least i has applications in the true world.

Utterly ConfusedSo James; you say: 0^0 = 0^(1-1) = 0^1*0^(-1) = ... = nullity. What about: 0 = 0^1 = 0^(2-1) = 0^2*0^(-1) = (0*0)*0^(-1) = 0*0^(-1) = 0^1*0^(-1) = ... = nullity.

Adammost computer programs will entrap the Division By Zero error and execute code designed specifically for such an eventuality. It's very very unlikely that programs will crash airplanes or desist a beating heart just because it hit a Division By Zero error. Software testers always test this eventuality and watch how the software behaves well before it goes to market. sum Dr. Anderson did was reclaim a designation to a concept that's otherwise known as the Division By Zero.

YabaTheWhatSomehow this all article feels enjoy a ploy to Get other people to accomplish Dr. Anderson's job for him. Numerous people absorb pointed out the flaws in the invention of "nullity", and a few absorb suggested more effectual functional alternatives (such as my earlier one, shown below because someone had the luminous thought of posting replies in invert order). withhold an eye out, as he may publish a paper in a year or two taking credit for ideas that appeared in replies to this article.

[Using the discontinuance of this message to contemplate if HTML code may be planted directly into responses to create paragraphs. Simply typing carriage returns doesn't work.]

Paul WellsEveryone should know that the BBC only likes arts and soft science programmes - so reporting something enjoy this makes them feel they understand maths.

Andrew P.I'm no mathemetician, but just at first glance I absorb problems with this. I guess one of my biggest "problems" with this...is that he appears to be treating infinity as a number. Infinity is not a number, but a concept. He has that 1/0 = infinity and -1/0 = -infinity. That's not quite right, because it's actually: lim x->0+ for 1/x = infinity and lim x->0- for 1/x = -infinity But at x = 0, 1/x is undefined. There is no simple algebraic equation (a+b, a-b, a*b, or a/b) such that the reply is "infinity". If you then wrangle that using limits you can sigh that his axioms hold...I would again disagree...because lim x->0 for 1/x = +infinity AND -infinity (depending on which pass you approach zero). (same for -1/x) If you accomplish select to deal infinity as an actual number, then the only pass his axioms actually hold is if infinity = -infinity...so that means 1 = -1. (not to mention countless other areas where treating infinity as a number messes things up...)... So if the axioms don't hold, well, anything you employ those axioms in really doesn't hold much water...If i'm wrong on this, feel free to revise me...

Jeff PeggThis is the stupidest thing that ever got attention! Period! You aren't doing anything innovative, you are just trying to Get your designation into the books. And a quote from the article is the worst. "We're the first schoolkids to be able to accomplish it - that's quite cool," added another. You are enjoy the first christians to be deceived.

bjrThere's too many comments likening i (sqrt(-1)) to this fresh Nullity concept. The difference, of course, is that factors i can be plotted as a sole point on a cartesian plane (it represents the non-real quadratic roots, which are useful in solving some problems) whereas nullity would be plotted by colouring the entire cartesian plane. There's lots of other high-fallutin' words flying around here too: non-euclidean geometry, transreal arithmetic. If this stuff is so abstract that someone with an undergraduate background in mathmatics can't contemplate how it applies to problems he's confidential with solving, why primary school pupils? absorb they absorb evolved some extraordinary capabilities which allow them to apply non-real mathematics to the true world? Or does it just fabricate a cute picture to launch this non-practical theory?

PMMy first problem is his assumption that 1/0 equals infinity, and -1/0 equals negative infinity. 1/0 does not equal infinity. 1 divided by an infinitesimally little positive number is equal to infinity. 0 is not an infinitesimally little number. To fabricate a random example, respect the mass of an "object". If the remonstrate has an infinitesimally little mass and a nominal volume, its specific volume (inverse of density) is considerably large (approching infinity as the mass gets smaller). If the remonstrate has a mass of 0, THERE IS NO OBJECT. Thus a measurement enjoy specific volume would be undefined, because the remonstrate doesn't exist.

Anonomous cowardThis is exactly the same as motto that the square root of -1 is i or whatever else you convoke it. It would be easier to just withhold it as (0/0) in equations without giving it a symbol (that is already in use). waste of time.

...really?With the birthright assumptions you can prove anything to be true...even if it's completely erroneous and/or inconsequential. 1/0 is not infinity. 1/x as x approaches 0 is infinity. They are two very different things. Faulty assumption = pointless proof.

John MeagherDr Anderson may absorb the birthright idea, but the naming convention is a shrimp off. According to Dr. Anderson, when you divide by zero, your reply goes to infinity (+/-), and covers a ambit of numbers starting with the next number beyond the numerator to infinity. However, "nullity" indicates a NOT anything, even though dividing by 0 is a NOT NULL answer. I'm not a math wiz, but it would fabricate sense to me if dividing by zero is soundless a controversy, then "nullity" would be a "not defined". By placing "nullity" outside of the number line, indicates the reply is soundless unknown. If the reply is unknown, then "nullity", with sum that the designation implies would be an inappropriate name. "nullity" would be appropriate, if the influence of dividing by zero results in zero (null). This tends to fabricate more sense to me: 0 x 5 = 0 0/0 x 5/0 = 0/0 5/0 = (0/0) / (0/0) 5/0 = 0 If 0 follows the conduct of little numbers, then the reply is infinity. If 0 is treated as null, then dividing by null is the same as dividing by 1; No influence on numerator as a given number over one. In either of these cases, "nullity" is not an appropriate designation for a not-null result.

Nathanso if a planes computer system divides by zero and crashes, we're sum gonna die BUT! if it divides by nullity and crashes, we're sum gonna die. wait...

JamesMany people posting here are showing a lot of ignorance about mathematics. It has been known for a long time that 1/0 = infinity and 0/0 is undefined. Conventional computer arithmetic can not cope with this. What Dr Anderson has arrive up with is a routine for allowing computers to accomplish computations involving these operations. However, it is so obvious that I doubt it has not been done before.

James HA lot of people posting here are showing a lot of ignorance about mathematics. It has been known for a long time that 1/0 = infinity and 0/0 is undefined. Conventional computer arithmetic can not cope with this. What Dr Anderson has arrive up with is a routine for allowing computers to accomplish computations involving these operations. However, it is so obvious that I doubt it has not been done before.

JamesA lot of people posting here are showing a lot of ignorance about mathematics. It has been known for a long time that 1/0 = infinity and 0/0 is undefined. Conventional computer arithmetic can not cope with this. What Dr Anderson has arrive up with is a routine for allowing computers to accomplish computations involving these operations. However, it is so obvious that I doubt it has not been done before.

Infinty and BeyondThroughout history the equation (n/0) = infinity. Surely he has just changed the designation given it a fresh symbol. PS can i absorb a reserch vouchsafe for discovering this nugget of information.

Reid NicholAll this guy has done is redefine what the true number line is and a few numbers. Let's retreat over his major mistake: inf \neq 1/0 To Get this one must do: lim_{x->0^+} 1/x Similarly for -inf. But one must note that if they approach 0 from the left then the badge flips. But that's another story. What he did was an operation that was undefined and define it without exploring any of the implications. This guy is playing with a fresh number line of his own invention. Also, this fresh number line has not been shown to be mathematically consistent in any pass shape or form. This guy should be embarrassed to publish this.

Mr. ner axiomnullity = sum the peoples in this blog.

taxi driverGet a true job giving handouts to immigrants instead of wasting your time growing a beard and mumbling enjoy an Open University presenter on BBC 2 in 1983.

A BritWhat is math?

BeauThese poverty-stricken kids. I just hope zilch of them reclaim this on their college applications under accomplishments.

GregorySo.. it took this long to invent another imaginary number? The square root of -1 is "i", and now they absorb another. I don't contemplate anything broad in this, just semantic gymnastics. Well done to this guy for selling it well though...

Extra dimension?The number line is linear. Add another line and two number lines gives us two dimensions. And finally add a third and there is their 3rd dimension. Now according to this "But Dr Anderson has arrive up with a theory that proposes a fresh number - 'nullity' - which sits outside the conventional number line (stretching from negative infinity, through zero, to positive infinity)." So does this stand for he establish an unknown dimension?

Dan JonesMy calculator doesn't give me an error when I divide by zero, it just returns "undef." It looks enjoy Texas Instrument figured out the solution long before this crackpot!

Patrick WeberHis interpretation is completely outside of the rules of mathematics1 How can this be useful1 If the final reply to a problem is "nullity" what does that mean1 Does it Get us any closer to understanding than 0/0; no1 What is "nullity" times 4- He had kids memorize that 0/0 could be written as a 0 with an I through it1 They absorb done nothing that Newton couldn't1 Throughout this post I absorb been using 1's in status of periods and -'s instead of question marks1 I just wanted to let you know that I absorb done something that Shakespeare never could1 I am awesome1

Ian BremnerHardly advice since mathematicians absorb been usng a similar routine to picture the square roots of negative numbers, at least they're hones about it and define the root of any negative number as 'i' - short for 'imaginary'

AnonI am but a child and contemplate enjoy a child. I am told that to unravel the equation 2x = 4, I can divide by 2 to Get x = 2. Thus 2 \times 2 = 4. Now I am told that I can divide by zero. Dr Anderson says so. So to unravel the equation 0x = 1, I must divide by zero to Get x = +infinity. So 0 \times +infinity is 1. Now let me unravel the equation 0x = 2. Then I Get x = +infinity. So 0 \times +infinity is 2. Now let me think. Oh yes then 2 = 0 \time +infinity = 1. Oops! gratify Sir, what absorb I done wrong.

ErikIf this man thinks he is some sort of mathematical prodigy, he needs to retreat seize his medication. And teaching this 'stuff' to kids is just outrageous. He doesn't actually accomplish anything other than sigh 0/0=0/0 and then give it a name, ha. What a joke.

BaruchThis doesn't fabricate sense. "Nullity" and zero may be different entities, but zero is the number that appears on the number line.

SoerenHe just "solved" the case 0/0, but not n/0 by using (valid) algebra rules. His "proof" is enjoy motto "8/4" equals 2, so everything else divided by 4 equals 2. This "nullity" is just another alias for 0/0, which has been invented many, many times before.

derpyeah because ya know, making your own "number" up and motto it's a solution is really mathematical.

DumbStruckIf one of his pupils came up with that in class, I am positive Dr James Anderson whould of told them off for wasting time. The alternative designation to Nullity is called Stupidity.

AbhiWhats the contrast between infinity and zero really ?

ZYour calculus professor would be very sad. =( gratify train the kids true mathematics and not some hoopla. Don't waste their time.

APBIf anyone has read down this far... I believe 'Sam' has it. In the "Proof", which is more of a sort of verification, (1/0)*(0/1)=0. But (1/0) is Nullity. So, in essence, he's using Nullity to prove Nullity. A broad no-no.

CordeliaWhy does the symbol for nullity examine enjoy a capital phi? And this is absurd.

Confused at MeaningHow about they just define 0^0 as some number? Then I can prove that 0^0 is that number that they defined. Yeay, I just solved the 0^0 problem.

MMI've seen an article on BBC motto that UK does not absorb enough scientists but I didn't realized until now that it was such a huge problem ...

Lost?Sorry, at what stage did this become advice worthy? Who exactly went out and scouted this story? Is this the future of TV, Web, Radio current affairs and advice programming? Dump this tripe and report on something that actually MATTERS! Otherwise I fright they will sum discontinuance up being divided by zero into an illimitable situation of apathy and incredulity towards the seemingly ever expanding "anything ‘ul do" advice culture....

h_mMaking up feign numbers = I ARE MATH SMARTNESS. I hereby propound a fresh number that is to be called "squnch." It has a value of 23, -78, Pi, and the color orange; simultaneously. Also, it is lemon-scented. I suspect that the proper employ of Squnchificonics will be able to unravel sum sorts of previously impossible mathematical problems, as well as leaving behind a fresh, invigorating scent. vouchsafe money now plx.

PythagorasBy the way, I lived around 500BC, so the problem is more than 1200 years old. Other than that, I can't foible this article.

Rusty ShacklefordWhat an utter waste of electromagnetic energy this legend is occupying birthright now. Amazing. I wish my boss worked at the BBC.

MarkHow does this disagree from i=SQRT -1, i is an imaginary number ??? Used in Calculus for YEARS !!!

Bryan WagnerThis theory is enjoy playing a game of "I win". Here's a generic algorithm: Let A be a proposition. "I win", therefore, "I win"! Oh my!!! P = NP!!!

chrisseiko flossberg, you just didn't Get it, did you... read the above article again and try to understand

FredrikHow can pacemakers divide by zero? I reacted, too. And of course, it's a MAN who comes up with this brilliant, simple idea.

Arvin DargfarthToo despicable you absorb the Moore and Anderson bits on ram files.. Could absorb been entertaining otherwise.

Dr James AndersenTo continue with my truncated comments below: the number 1/0, is, by my definition, > 2/0 or 10/0 or 10000/0 or indeed, 0.2/0. Therefore it follows that 0^0 = 0/0 - a class of 10 year olds has followed this. If they can it should be simple for others.

Cambridge Maths PhDIn fact there are ways to deal with infinities arising from division by zero (in some sense), but, as far as I am cognizant not by adjoining the true line with a fresh number (to accomplish so looks suspiciously enjoy taking the true section of the Riemann sphere). The matter of 0/0 is soundless undefined in sum these approaches (the definition of a system of arithmetic is that of a mathematical field, and the field axioms leave this undefined. One would absorb to employ a different definition of arithmetic if you want to Get around that). Mathematicians in the terminal century discovered a fresh system of arithmetic that is a generalization of the true numbers, these are the surreal numbers (there is quite a large literature on the web). Related to this is non-standard analysis which makes employ of similar quantities to develop an algebraic calculus. Roughly, true numbers are defined by a Dedekind cut, that is by taking the rational numbers on the number line and diving them in two. Surreal numbers are defined similarly though in terms of a lop of the surreal numbers themselves (so it's a recursive construction). The surreal numbers contain non-zero numbers that are smaller than any true number, and others that are larger than any real. In this pass infinitesimals and infinities can be dealt with algebriacally (an infinitesimal might easily be mistaken for 0 if they thinik only of the true numbers), though division by it is soundless well-defined. sum very elegant, but whether Dr Anderson has rediscovered this or someting similar, I wouldn't enjoy to sigh as I can't download his proof.

CPBrownFairly simple from the article. I would adore to contemplate the paper he produced though. It will fabricate their maths considerably different to before.

PC userIf Dr Anderson is from CS department would he not already know that PC's absorb NaN for divide by zero problems?

Dr Roy JohnstoneI am a lecturer in the Department of Mathematics at Reading University. I wish to distance myself completely from the utterings of Dr Anderson. He is NOT a member of the Mathematics Department and cannot picture the views of the Mathemtics Department. The thought that dividing by zero has been an unsolved problem for mathematicians for hundreds of years is laughable. His `solution' is nothing more than the unnecessary employ of terminolgy to indicate that a division by zero has been attempted. The promotion of his ideas to school children is likely to fuddle rather than enlighten them. He is being very irresponsible.

Tungsten (born in a Meteor)If Dr Anderson's axioms are indeed consistent with arithmetic as he claims, then you can employ his axioms to prove in 3 lines that Nullity = 1 and Nullity = 0.. in other words that 0 = 1. I'm joyous that most comments below are critical, it shows that people can soundless contemplate for themselves and not be dazzled by semantic sleight-of-hand. In other words, this is grade-A applesauce.

AndriyAbsolutely despicable theory. Has nothing to accomplish with true science. Demonstrates very poverty-stricken smooth of the guy. The theory will completely fail if it is used in calculus. Indeterminate forms of sort 0/0 (when one looks for circumscribe of quotient of two vanishing functions) cannot be evaluated enjoy some universal symbol. That's where calculus started its evolution (by smart guys, not enjoy this one). I want to contemplate him flying in a plane desinged using his theory. And his (antiscientific) theory is really confusing for 10-year children. One should interdict him from teaching in school - otherwise he may spoil a future mathematician or engineer.

Kartik KrishnanIf this was the case a zillion pace makers would absorb already failed and aircrafts crashed...thereby killing people. besides computer systems are quite advanced to handle infinity (this is what they Get when they divide a number with zero)As if you contemplate the smaller the fraction of the number you divide a number with the result is a huge number (so infinity)

BruceThe fact that he preached this drivel to kids instead of Mathematicians pretty much says it all. They were the only audience that would not burst into laughter.

Doctor ScienceI contemplate he is making something out of nothing.

benjamin sanchezwhat he says is not posible beacuse 0^0=e^(0*log(0)) and log(0) is undefinied at zero (goes to -inf), what he proposes is just a diferent notation to something that can't be done.

ranatalusImagine that, they solved a mathematical impossibility by creating another imaginary number (such as pi, i, and infinity).

MattAmazing breakthrough! Congrats. For sum you university of reading computer science folk here is a nice patch to fix sum the mission critical systems you're running! #define NULLITY NULL

NonnyWell this is distinguished fun. Those who remonstrate to Dr Anderson having merely stated a tautology surely pay him a compliment, since sum of maths is one broad tautology: ie what follows from the chosen axioms is what follows from the chosen axioms. But the altenative of axioms is a significant question; if those listed in Dr A's paper on transreal numbers accomplish indeed contain sum true arithmetic as well as absorb some extra benefits, then safe on him. Unfortunately I am not ingenious enough to know if they do, so they should await some proper peer review of his papers before dismissing him completely. Wasn't the square root of 2 initially rejected as heretical? (I believe someone was killed over that heresy).

MathemagicianWhen a computer program tries to divide by zero it will be imformed by the operating system that this was an error and the program can employ this information to avoid continuing on with some crazy result. Only poorly written software will actually crash. You can create a mathematical system whith whatever concepts you want such as infinity however this doesn't stand for they absorb any relevence to anything in the true world Just my 2 Nullities.

BobIts not a proof. He's just motto that 0/0 is something and he calls that something nullity. Its enjoy sayin 0/0 = x. Theres no actual value to it.

Richard LeeNullity sounds enjoy just another pass of motto "Damned if I know!". The Prof is attempting to create a fresh symbol where there is no need, they already absorb a suitible symbol and its already in common usage "?". Seriously though, has it not occured to anyone that 0/0 doesn't actualy absorb an reply because it is a nonsensical question.

Prof. Pedro Carvalho BromOk. But as to explain these activities of the zero in complex plain? After sum its the zero that transforms C in to R

Robert NewsonClearly Dr Anderson is a feeble mathematician. It's scandalous that he gets to train this nonsense to schoolchildren. Dividing by zero is a problem because they define division, in gauge mathematics, as the inverse to multiplication. There is simply no value that you can multiply zero by to achieve any other value. 'Nullity' solves nothing, the man is a fool.

Mr sort CastAll i can sigh is 0x00544e5543, retreat figure! (the clue is in the name)

David EIs this a joke? Basically you're motto that 1/0=A where A=1/0. Congratulations genius..

Maths ManThis is not maths. I've heard that this guy is a running crack in the University of Reading Mathematics department. gratify check your stories with informed academics before making fools out of yourselfs.

Matthew GrayboschWhen I studied maths in school, I was taught that the result of a divide-by-zero operation was "undefined". Dr Anderson's theory makes sense, but when I'm coding, I'll withhold putting in code to entrap divide-by-zero attempts and deal with them.

Ummm...why don't they just program the computers to recognise zero as nothing? It's not infinite, it's NOTHING!!

sleeki absorb a better word for it. how about flooglyflop? what a stupid article

He forget to designation the "Theory"It's called : "sensationalism". Dr Andersons "nullity" is not a theory nor some "new thing" let along any concept that could aid software engineers, trust me. This is not a theory, just the mere introduction of a fresh symbol for something that already exists, and which obviously journalists fail to understand.

Master DanBreakthrough!!!! I absorb solved the problem dividing 2/3!!! Finally they dont absorb to wright it in fractions or aproximately 0.333333. My distinguished discovery is this 2/3=¤. From now on,insteead of writing 2/3, lets print "¤"! I cant wait for BBC to arrive knocking on my door!

GazI'm no mathmetician, but, not wanting to spoil "established mathmatical proof", surely sum those who are motto "1/0 = infinity" absorb lost the plot haven't they? Surely that would stand for that "1 = infinity * 0" and then "1 = 0"!?!?!

Someone with a degree1/0 does not equal infinity. It is 'undefined', and for safe reasons. Division is based on multiplication, where x/y = z besides means that z * y = x, in this case infinity * 0 = 1, which is false, which obviously foils his axioms. Moreover, infinity is not a quantity, and is not allowed in arithmetic because you cannot apply sum the basic principles to it. Example: a + b = c, a + d = c, then b = d. if infinity + 1 = infinity, and infinity + 2 = infinity, then 1 should equal 2...this is why infinity is not used in arithmetic. His 'theory' will not stand up for a second in the mathmetician world. Sorry you were sum duped.

Bill HannahsWhat exactly is 240 times null? Get back to me when you figure this out. A fresh problem is created by the null solution in the value is passed... how is the computer going to handle arithmetic computations on null other than crash? Nulls are a true pang to drudgery with as it is and usually you not only code to handle division by zero errors but besides for errors involving functions on null which are frequently more difficult to write than for division by zero. This solution really opens a can of worms: you'd need to rewrite sum arithmetic functions and most code which uses these functions and you would discontinuance up with an even less stable system than if you just dealt with the error properly.

MaheshNothing fresh here. traditional theorem, fresh packaging. Publicity stunt.

reykngWhat's in a name? that which they convoke 0/0 By any other designation would be just as false; So 0/0 would, were it not 0/0 call'd, Retain that dear falsehood which it owes Without that title. 0/0, doff thy name, And for that designation which is no fraction of thee seize sum my PHI.

98abaileSo its invent a number time. In which case I propound that 2-1="dog" Discuss.

pixieYou can't employ 1/0 in your equation to define 1/0. That's going round in circles!! No pun intended.

Clive PageAs many others absorb pointed out, most modern computer processors employ IEEE 754 arithmetic in which 0/0=NaN. But he does absorb a point in highlighing the need for fail-safe software: the first launch of the Ariane-5 rocket by ESA failed because of a numerical overflow in the guidance system. The system detected it and switched over to the spare, which of course performed the same calculation, and there was another numerical overflow a few milliseconds later. The rocket had to be destroyed over French Guiana at enormous cost.

April WinterbottomSorry. It is soundless December.

TheEngineerThat's not solving - that's a definition and a circular evidence. Nothing's been proven.

pauldmy friend's pacemaker divided by zero and stopped working 2 years ago. They did implement fresh technology where it wouldn't accomplish that anymore.

Jacques BourquinThere actually is some verity to this document. Let's suppose for a flash you absorb 1/0, (or 2/0, 3/0, n/0) which essentially equals infinity, recollect that infinity is a condition, not a number, that's why they can sigh this, because they aren't expressing a finite quantity. So let's accomplish some simple algebra and they Get 0 = 1/infinity = means 0 = 1/(1/0) = 0/(1/0) = 1 = 0 = 1, so essentially by trying to express 0/0 as number you are motto 0 = 1. But wait, they erudite in fractions that any number divided by itself is 1, but earlier they just said any number divided by 0 is infinity, so, which is it? Does 0/0 = 0, 1, or infinity? Therein lies the problem with 0/0, in calculus they convoke this an indeterminite form, because its value cannot be determined. Class dismissed.

Larry VInitially, I thought this legend was a crack article. Really. I looked around the page for something enjoy "Today's funnies." Failing at this, I'm forced to accept that this is perhaps TRUE. This is ridiculous. Just making up a fresh number doesn't unravel anything. They already had something that represents this sort of idea: "NULL."

Mike"Thou shalt not divide by zero, lest thee bringeth a mighty tragedy unto thine land."

CCWhat a cop out, this isn't solving a math problem, he just thinks he is being clever, by using a "symbol". Wow, well I will redefine math too. 1/2 is nolonger 1/2 but !@. Recognize my skills!

DrewUmmm... My terminal post hasn't shown up yet, but in case it does, I made a typo. 5/1 is 5 because 1 can retreat into 5 five times not 1 time. :-)

John WallisI came up with this in the 1600s, and I picked a better symbol!

ShabazI'm pretty positive my Maths teacher came up with something similar. Then again, he couldn't spell "bigger". Actually, he looks a bit enjoy like THIS crazy dude.

my designation is NEOwell given this i can fabricate up results enjoy 0 * infinity = nullity and 0*-infinity=nullity and withhold on going... so nullity is soundless undefined, which is what I learnt in the first place. So whats new? the word??

Forget 1200 years, BILLIONS!Why 1200 years? This has NEVER been solved until now. So, they should sigh 4.1 Billion years (perhaps longer...). Whoa. I can't wait until they integrate this theorem into airplane autopilots... and nuclear missle launch systems. They really need it there. "My game's enjoy the Pythagorean Theorem. It ain't got no answer." - Shaquille O'Neal

Keith BraithwaiteOh dear. The days are long gone when attempting to divide by 0 caused computers to "just desist working", and many programs that accomplish numerical drudgery already employ a value called NaN (for Not a Number) to handle the results of such operations.

Um..N/0 = UNDEFINED. He just renamed UNDEFINED = NULLITY. I contemplate this as a publicity stunt rather than honest mathematical news.

sonjamy problem is that I cannot except the zero exists at all

???N/0 = UNDEFINED. He just renamed UNDEFINED = NULLITY. I contemplate this as a publicity stunt rather than honest mathematical news.

ComSciNullity is already defined as a yang to a kernel’s ying. To sigh yang exists is to define ying as Nullity. So only in the {} this is true. As {} not equal {0} then the theory is false. Shame on you people for mixing apples and oranges for the ignorant.

DrewI'm surprised at the comments that sigh something enjoy this: There are 5 apples and 5 people. 5/5 is 1 because each person gets one apple. There are 5 apples and 1 person. 5/1 is 5 because each person gets 5 apples. Also, if there are no people, then 5 apples are left so 5/0 is 5. NO! You're assuming that something is happening to these apples if there is no people. It's called division for a reason. The traditional reply would sigh that it's impossible to define this scenario because "How can you divide 5 things among 0 people?" The fresh definition is this: 5/5 is 1 because 5 can retreat into 5 one time. 5/1 is 5 because 1 can retreat into 5 one time. How many times can 0 retreat into 5? More than 1? Yes. More than 5? Yes. More than 700 billion times? Yes. The reply is infinity. BTW, don't they already absorb a symbol for infinity? It's a sanguinary sideways 8!

Someone with an actual degreeAttention whore....sigh.

US GringoIf it's a 1200 year traditional problem, then how did Pythagoras (b~ 570 BC) retreat over 1500 years into the future to try to unravel it? entertaining read nonetheless...

J.D.Bailey1>0>-1, sum are knowns ...-1<...0... sum are known from a practical perspective. they absorb always had an application problem dealing with the unknowns. applied and abstract math accept that there must drudgery significant weight is fact existing unknown surmise which accomplish their best to cope. at macro smooth reasonably speculate hypothesize objective observational knowns. zero one time was not in mathematics ... i know what may be accepted this or next millennium but very broad aid maybe something identifier overlooking need define foster science math. anyway reasonable analytic defined today does unknowns for tomorrow. ps god mythology></...0...>

MattHe didn't unravel anything. Now they absorb a symbol for nothing. Great. safe work.

Kate MeloneyAre you kidding me? It has no status on either the real-number line or the complex plane. What happens to Lim h-->0 (0/h)?? It's value is zero, but at h=o, suddenly it skips to some Nullity number? No...this doesn't work.

JoshDr. Anderson has done a really ingenious thing. The same pattern of discovery and progress was made when the symbol for zero was invented. So what he did was essentially the same: employ a symbol for something counter-intuitive or previously unrepresented in calculations and formulas. Intelligent.

Robin PIt sounds do-able, but seeing as this is an older article and it soundless hasn't made headlines or changed the Calculus books around the world, I am thinking that it has been disproven, or at least, has too many flaws in it and needs to be more defined before it can be called a theorem.

Johnny Cash from beyond the graveThe thought is stupid, you can convoke dividing by zero whatever you want. His thought of 'nullity' is something mathematicians already understand and are constantly tackling with. His thought really is to let computers deal with dividing by zero. He hasn't answered any questions about dividing by zero.

JesperThis is just unadulterated nonsense.. A problem that Newton and Pythagoras could not conquer..? Yeah, right.. The thought of introducing a symbol for the operation of dividing by zero is very traditional and simple. It is in no pass revolutionary and has nothing to accomplish with difficult unsolved problems.

DenxI want to believe Dr. Anderson is confidential with the classic comic routine where Lou Costello shows Bud Abbott that 7 * 13 is 28 via addition, multiplication, and division.

gBHey, did you people know that 22/7 is a pretty safe approximation to pi? Its pretty neat, I employ it sum the time when I program stuff in languages where I dont know how to convoke on pi. My simulations are off though, but it compiles :S. So accomplish I Get a price?

Matt EustaceIt is so incredibly simple to prove this thought wrong. In fact, the proving wrong of this is actually covered by the syllabus of A smooth further maths!

SaroThis is useless.

MikeSilliness. Division by zero is 'impossible' because there are an illimitable number of revise results, not because they were lacking some stupid fresh symbol to picture it. I challenge the professor to bring that to the entire educational community and contemplate if he A) wins the Nobel, or B) gets laughed out of the building.

dan allfordthis is definatley the stupidest thing i absorb ever heard. if this is what you convoke x/0 then it is soundless undefined.

DanSo he just invented a number to unravel the problem? How is that math? Why not convoke it X where X=0/0. It's nonsense. Besides, 0/0 = infinity.

MGIt looks enjoy the guy just came up with a symbol to picture the impossible equation of 0/0. This seems neither novel nor interesting.

RobFor sum they know: 1/0 == chicken. I conform with sum those who absorb said that he has just renamed the solution - this is not a fresh idea.

TheOddManEverything to the power of zero equals one! Everything divided by itself equals one. This guy has solved nothing at all. Just supersede nullity with 'one' and it'd fabricate even more sense.

alan r. math gradI am very interested in reading Dr. Anderson's paper when published. But what strikes me most entertaining is that there are so many extremely stalwart reactions against his idea. Obviously it has struck a chord with a lot of people and that often happens when a long standing thought is challenged. (At one point in time not too long ago it was just taken as fact that the sun revolved around the earth. Challenging that thought could absorb resulted in your execution.) Unless you absorb already read his mathematically rigorous theory and proof as would be published in a paper and establish a rigorous flaw with it, i contemplate it would be premature and immature to bounce his thought or refer to designation calling. Mathematicians should absorb no reason to feel threatened by his proposition if indeed it is "so obvious that he is wrong." But it appears that most of the comments are intended to accomplish just so after only having read an article written in layman's terms. Number fields are defined by axioms - if he has been able to define a set of elements that adhere to the axioms, then would be nothing mathematically incorrect with his arguments. I absorb not seen anywhere where he has stated that nullity lies in the true Number field; thus it does not "break" the arithmetic of numbers most people are confidential with. He is in fact motto that nullity "sits outside the conventional number line." The problem is that it may be very difficult (albeit not impossible) for the mediocre person to arrive up with a metaphor to aid them understand nullity. For example, you don't absorb to understand the Rational Number field to know that 1 apple plus 1 and a half apples is 2 and a half apples. People often employ this lack of understanding to give themselves permission to employ the perverse justification: "If I don't understand it, it must be wrong/he must be an idiot." Dr. Anderson has an entertaining thought and once formally defined then it should be reviewed critically.

SVOh distinguished next time check something enjoy this with someone who is certified in maths by a university. I stand for this is nothing else then what the IEEE defined as NaN (Not A Number) for computers. The reason for calling it not a number is because it can be litterally any number and it is unknowable which number. Thus anything that would be unsolvable prior to inventing nullity would soundless be unsolvable due to the inability in translating any result that uses nullity to a number because you absorb to translate this solution to every number.

Bigger problemWoW! So they establish out how to divide by zero now they absorb another problem. How accomplish they Divide by Nullity. accomplish you contemplate were this is going?

BlackTiger™"nullity/nullity = 1"?!?!? Ofcoz NOT! X + nothing = X X - nothing = X X * nothing = nothing X / nothing = nothing nothing / nothing = nothing There must no be terms enjoy "negative nothing". "Nothing" cannot be negative or positive because it's just nothing. Actually... I abominate mathematics and abstract physics. Because of stupidity. These "sciences" replete of ersatz crap. Yes, some ersatz constants can drudgery for known(!) problems. But who said what they know everything? They are dust in the Universe!

Jason Jacobsfor a computational system to be 'universal' they must be able compute the reply 'undefined'.. if sum answers are definable then the computational system is not 'universal'.. this nut job has 0 understanding of computation. He should read turings papers on computational universality..

Oh DearThe comments above sigh it all. BBC, shame on you. You are truly an embarrassment.

TiagoDr Anderson's concept is exemplar for people who suck at calculus. Nullity does not unravel problems, just avoids them. When solving a calculus problem, reaching 0/0 forces you to find the PROPER solution for the problem, using a number of theorems developed throughout the centuries, those actually designed to unravel the problems at hand. faineant programmer.

Kristopher Kirkland1) Before bashing this man's intelligence or his theory, gratify actually read his work, rather than what boils down to drivel and a photo op (you wouldn't trust the local newspaper to perfectly explain Einstein's Theory of Special Relativity). 2) Most program are engineered not to encounter a division by zero, however if one occurs, an exception will occur, an depending on the machine, it may crash. 3) sum your proofs of how his theorem sigh infinity=0 seethe down to using something enjoy 1/0 * 0 = 0, however this could be rearrange to 0/0 * 1 which equals -0-. 4) NaN and indeterminants are not solutions to the problem of 0/0, they are drudgery arounds. Ways of avoiding dealing with the 0/0.

MatthewWow, so now my pacemaker's going to crash with an 'unexpected null value' bug instead of a divide-by-zero bug! Revolutionary stuff eh.

ClayCool, so can I publish my theory about 7 being the terminal digit in pie? Don't belive me...disprove it :P

MathieMaplesoft (creators of Maple) solved this problem a long time ago, they employ the word Undefined. Or the word infinity if the circumscribe actually approaches the same infinity from both sides. I absorb no thought what this guy thinks he is doing, but it doesn't accomplish anything. When you divide by 0, you absorb two choices. If the division by 0 is done by having a simple polynomial approach 0, you can seize the circumscribe and drudgery with that. However, if the circumscribe is undefined your computer program has to give some sort of error otherwise sum results after that point will be guaranteed to be wrong. This is simply from the fact that in a structure which repeated calculates something, if I hit a point where my variables are undefined, I am screwed. I need to throw an error and then try to employ some other routine to determine a pass to redefine my variables again. This is especially vital if I am dealing with a real-world scenario enjoy medical equipment. In Maple, they employ a term called undef, which basically has the property that any arithmetical operation done to undef remains undef. Which is completely and totally useless, because (if this was a medical computer, for example) that does not relate me if my patient is soundless alive or not, or how much medication to apply to him. It besides does not relate the programmer whether or not they need to entrap the error and deal with it. So basically, this nullity is either a fresh word for undefined/infinity or something even more useless (and uncertain if used). BBC should be ashamed for publishing this tripe.

JonathanSo essentially we're taking the set of things that are undefined and calling it "nullity." This is fresh and incredible how?

TheoIt appears he's just taken an element of Calculus (lim x->0-) and arrive up with a fresh designation and symbol for it for employ in algebra. And it has no true employ for computers; it'll only result in a software entrap to fabricate positive that when 0 occurs in a divisor, a different logic path is taken. And we've been doing this anyways.

Brian MatthewsI find it very worrying that this is being presented to schoolchildren as fact. There is enough mathematical illiteracy without this mountebank adding to the problem.

Armend AdemiIf I absorb 10 oranges and will participate them with 1 person(10/2=5)I will Get 5 oranges. But if I don't absorb no one to participate oranges with (10/0=10)than I will Get sum of them, 10. In that case I contemplate 0 enjoy 1:)

some americanHey, I've got a proof that holds just as much weight. ... = 0/0 = 5 Therefore, division by zero equals five. relate your friends.

KermsWow, personally i am impressed. I should absorb scribbled on a paper and submitted it to BBC years ago with an = 0*0 next to it.

anonymous cowardthis legend is of singularly (no pun intended) stupid quality. mathematicians have, since at least riemann, had no wretchedness dividing by zero when it was needed and in some legitimate. in fact, introducing a symbol for 1/0 is usually referred to as adding a point at infinity (for obvious reasons) and is a technique introduced to undergradutes. this is not news.

Simon HastingsI don't know if this has been commented to(since there are alot of them), but the reason deviding by zero is undefined is not because they can't find a definition for the results, but because they can find TOO MANY definitions. seize A/A, where A equals zero on the top and bottom. Now circumscribe them as A goes to zero - the result seems to be 1! Likewise -A/A seems to produce -1. Seems Fair. What about 1/0 from the left - whoops, negative infinity, and 1/0 from the birthright gets us positive infinite, and 0/A from any direction gets us Zero. So what accomplish they fabricate it for sum cases? No idea. Thats the true issue.

Eric TowersThe arguments of the form, "He just made up a fresh number. Bah! How useless!" are amusing in the context of mathematical history. Similar comments were made for negative numbers, irrational numbers, complex numbers, transcendental numbers, et al. Much growth in mathematics has arrive from taking a step back and accepting more things as numbers (and making up symbology to label the fresh numbers). So this shape of knee-jerk reaction is pretty funny. I am concerned about Dr. Anderson's displayed proof. The production (0/1)^-1 --> (1/0)^1 is on shaky ground (without more explanation) since it requires a theory of division and division is the operation that is being modified in this extension. Also, the title that the set of axioms with the nullity axiom(s) added is consistent is probably weaker than stated in these comments. At best, the statement could be "arithmetic + nullity is as consistent as arithmetic". Godel has convincingly argued that they will never prove the consistency of arithmetic or any system that contains (i.e. can represent) arithmetic. So, the highest attainable shape of consistency for such a theory is "at least as consistent as arithmetic". Regarding the question of "division by nullity", application of the axiom gives (for sum x (including the three fresh symbols), and using "O" for nullity): (x/O) = (x)^1(O)-1 = (x)^1(O)^1 (because (0/0)^-1 = (0/0) by the syntactic transformation (a/b)^-1 -> (b/a)^1 ) but this is (x*0)/0 = 0/0 = O. Explicitly (re-)checking the fresh symbols, only the step x*0 is interesting: (1/0)*(0) = (1*0)/0 = 0/0 (-1/0)*(0) = 0/0, similarly (0/0)*(0) = (0*0)/0 = 0/0 So the proposed extension seems to provide closure under division. I'm concerned that (2/0), (3/0) et c. nonstandard numbers are not defined. This worries me because this extension looks a shrimp enjoy nonstandard analysis of infinitesimals "inside out". I.e., where the dualities (nonstandard infinitesimals

AndreyQuite stupid. This introduces zilch of a concept, just a fresh symbol that means nothing.

SamuaiI contemplate this is just great

DarthIke7This is the same thing that everyone has said but here goes anyway. This theory has been around for a long time. It reminds me of the theory of imaginary numbers. The problem is unsolvable, so a number is made up that solves it. A NAN number. you can't define infinity as 1/0 because illimitable has no definition other than that it is endless. This dispute is just enjoy the people who wrangle over how proximate a googol-plex-plex is to infinity. A googol-plex-plex is the same distance from infinity as 1 is, because infinity is endless, it has no exact value. I'm sorry Dr. Anderson, but you just got OWNED!!!!!!!!!!!!!!!

MallReviews.comOne would hope that auto-pilot and or pacemakers absorb their calculations set to workaround the "divide by 0" catastrophe renowned by this teacher(?).

jamesThis is a very traditional thought that has been fraction of computer science and electronics for many decades. Computer Sceince has had the value NULL for over 20 years. Electronic equipment has had tri-state boolean values 1,0,OFF for even longer.

RG4 MANDEMThis makes me ashamed to sigh I arrive from Reading. :'(

GlennRealplayer has just crashed on me with a divide by zero error! How?????

KJExactly how much does this university pay this guy to clearly accomplish nothing sum day? "Imagine you're landing on an aeroplane and the automatic pilot's working," he suggests. "If it divides by zero and the computer stops working - you're in broad trouble. If your heart pacemaker divides by zero, you're dead." So you check first to fabricate positive you're not dividing by zero. And then what? The autopilot says, "nullity." Your pacemaker says, "nullity." Yer dead anyways!

JacobI wish my lofty school math teachers had been this open-minded. Making up solutions on the Fly would absorb seriously helped me in Calculus.

Tom RitchfordUm, you perhaps need some editors with a better grasp of mathematics and its history. The specific thought of enhancing the number line with a positive and negative infinity is well over a century traditional and was neatly formalized as fraction of Abraham Robinson's theory of infinitesimals half a century ago. This isn't particularly obscure stuff -- first year University students absorb been taught calculus using this method. The "nullity" thought appears to be just plain wrong. You can certainly add any symbol you enjoy to picture 0/0 (though phi is a poverty-stricken altenative as it already is used to picture the Golden Ratio). Unfortunately, you can't give this fresh "nullity" number any sort of consistent behaviour when you add, subtract, multiply or divide by it -- it's more enjoy a symbol meaning "put down your pencil now". Mathematics has besides had this exact thought for centuries now -- the result of this calculation is "undefined". This is what I was taught in primary school many years ago. For Dr. Anderson to title that he has solved a problem that has lingered for 1200 years is hubris, plain and simple.

MattI tried to convince a teacher in HS that 4.pi was a number... she didnt buy it. Maybe this guy can arrive up with a theory for it to aid me out!

JBZero divided by zero = nullity? WTF? 0/0 = 1 1/0 = 1u 2/0 = 2u 2u*0 = 2 That makes a lot more sense.

BobWhat is Nullity/Nullity ? What is Nullity X Nullity ? What is Nullity^Nullity ? What is 0^Nullity ?

Vic SnowdenI can finally sleep!

AimeeCan you not sigh "20 divide by zero equals zero rest 20"? That makes more sense to me.

Ewen MallochSo 0/0 is nullity which can be drawn as a point above or below (or left or birthright presumably) of the number line. Geometrically, this implies it has a length - a distance from 0, similarly to i having a length of 1. So there must exist a value twice as long or twice as far from 0, so 2*nullity (compare with 2i). 2i can be represented as the square root of -4. What can 2*nullity be represented as in terms of the number line? Is it soundless 0/0? If so, surely you've defined a singularity as sum points expressed in terms of "nullity" can be represented as 0/0. The references to getting "errors" when computers divide by zero is just poverty-stricken programming. Yes, it produces an error by the code should resolve that error cleanly - by defining it and an action to take. How is that different to a definition of nullity or NaN?

HeIsRightAll you people that discredit this are just covetous fools who wished you thought it up first. So retreat back to your cavity and sit down and shut up.

KevmanSo, will the IRS allow me to submit a nullity return?

CoolWow..1+1=Unknown

Content FreeYou absorb failed to present how assigning a symbol to positive and negative infinity changes anything, other than the student's capacity to write the symbol in status of "undefined".

TokkanjinAnother silly theory: 0/1*1/0(As above) =1/infinity*infinity =1 ohh which is what sum other numbers are to the power of 0. Therefore according to the above 0/0=1 so nullity=1 therefore according to this you absorb reinvented 1

GurrahBeautiful ! Congratulations ! The numbers of variations of an innumerable set of problems might now drudgery out to become practically possibilites for anything from physics to mechanics. A distinguished great breakthrough - If I had a sigh I would convoke it Nobelprize-worthy !

NictitateWhat's Pi in binary?

l0rd_4thl0nBravo to Dr. James Anderson. Your drudgery is simply excellent, even if these self-professed by sentiment "experts" can't comprehend the consequences of your vital discovery. I will be following your drudgery further.

Felix PerssonDid Pythagoras live 1200 years ago?

Suprised Swiss Computer ScientistAhem ... I _think, 0 to the power of 0 is 1, and not Nullity (whatever that's suppositious to be). This all thing is ridiculous and there could only be one day in the year where I would understand this appearing on the BBC web site, which is April 1.

George CookRead chuck norris's ninja comment. Thanks chuck - elegant and insightful - this "professor" would be much better teaching his calss your way. besides - I hope that the year 13 stats comment was not someone in his class.!?

Real simpleso, nullity? ok, on a true computer, if you wanted to prove nullity (or non-trueness), convoke it NULL or NIL. x / 0 = NIL there is your nullity birthright there. wha does it solve? nothing, since nullity is itself undefined.

Don PhilipThe mechanics of the theory itself are simple enough to understand as far as he has presented it. However, locating a number off the number line is the problem, and to fully understand what he has done, one would need to understand the mathematical justification for being able to accomplish so. Otherwise it's a shrimp enjoy motto that you've arrive up with a fresh number (we'll convoke it snark) that equals the square root of negative 1. Without a proper justification or proof, it's just a word with no meaning. Dr. Anderson needs to fabricate his proof more limpid before I can accept this.

Forrest GumpMama always said... Nullity is as nullity does...

KimThis has to be a joke.

A Random Smart personDear sir, trying to Get your designation in the history books by motto nothing is nothing will not work. You create this highly obstrusted math to try to present something that is to be something it isn't. N/0 = undef for safe reason. Trying to sigh 1/1 = 555555/555555 its honest but it isn't so. safe day.

DaveAPRIL FOOLS! - Oh wait, its December.

Tom Horseonovich ColliganI absorb followed this thread with interest, and conform that perhaps the best forum for exploration of a fresh theorem is not in a classroom of puerile students, but before a curious and critical group of advanced mathematicians. Though there are issues with this fresh theorem which materialize to render it erroneous when examined in a purely mathematical context, I accomplish contemplate value in exploring the possibilities of "nullity" within the realm of computer science. Tom Horseonovich Colligan Rouse Ball Professor of Mathematics Cambridge University

Alex ZavatoneI don't understand it because I can't contemplate the video. gratify employ some cross platform video file format enjoy .mp4 so more people can view the video

norwegian guyThis is an traditional "solution" to the problem, it has just not been accepted as a solution. Imaginary numbers (numbers which sits outside the conventional number line )has been used for hundred of years in calculating negative square roots and equations that absorb no solutions. But its soundless not a safe solution to a problem, as the calculation is not workable using "accepted" mathematical methods.

alan r. - math gradI am very interested in reading Dr. Anderson's paper when published. But what strikes me most entertaining is that there are so many extremely stalwart reactions against his idea. Obviously it has struck a chord with a lot of people and that often happens when a long standing thought is challenged. (At one point in time not too long ago it was just taken as fact that the sun revolved around the earth. Challenging that thought could absorb resulted in your execution.) Unless you absorb already read his mathematically rigorous theory and proof as would be published in a paper and establish a rigorous flaw with it, i contemplate it would be premature and immature to bounce his thought or refer to designation calling. Mathematicians should absorb no reason to feel threatened by his proposition if indeed it is "so obvious that he is wrong." But it appears that most of the comments are intended to accomplish just so after only having read an article written in layman's terms. Number fields are defined by axioms - if he has been able to define a set of elements that adhere to the axioms, then would be nothing mathematically incorrect with his arguments. I absorb not seen anywhere where he has stated that nullity lies in the true Number field; thus it does not "break" the arithmetic of numbers most people are confidential with. He is in fact motto that nullity "sits outside the conventional number line." The problem is that it may be very difficult (albeit not impossible) for the mediocre person to arrive up with a metaphor to aid them understand nullity. For example, you don't absorb to understand the Rational Number field to know that 1 apple plus 1 and a half apples is 2 and a half apples. People often employ this lack of understanding to give themselves permission to employ the perverse justification: "If I don't understand it, it must be wrong/he must be an idiot." Dr. Anderson has an entertaining thought and once formally defined then it should be reviewed critically.

A. CarantiI read one of the two papers Dr Anderson co-wrote, and it seems to me that once you Get Phi (the "nullity") in an intermediate step of a calculation, you are stuck with it for the rest of the calculation, in the sense that every operation that involves Phi will always give Phi as an answer. So what would you enjoy better, a computer that works for an hour, and then gives you Phi for an answer, or one that after a minute or so tells you "Look, Doc, you just asked me to calculate 0/0: you want me to withhold working for an hour, and then give you Phi as an answer, or perhaps you prefer to reconsider the programme you asked me to run?"

Seiko FlossbergGood idea, because it happens sum the time that pacemakers divide by zero and desist working. In case you didn't notice, I was being sarcastic.

JamesIf Dr Anderson's axioms are consistent, and more importantly as far as mathematics is concerned, novel, then he deserves congratulations. I don't contemplate any employ for them currently, but that doesn't stand for there isn't one! Other extensions to the excepted set of numbers were besides thought to be useless at the time (I'm thinking of imaginary numbers), but became hugely useful later.

PKAre you actually motto division by 0 is possible? Because writing 0/0 presupposes that division by zero is possible. If so, respect the following: 1*0 = 0, so 0/0 = 1 2*0 = 0, so 0/0 = 2 3*0 = 0, so 0/0 = 3 etc. If division by zero i So does "nullity" = any number I want it to equal?

B1Division is just a short-cut for subtraction; any problem becomes: 'How many times can you subtract x from y?' An the reply to how many times can you seize nothing from something? Is infinity.

Ranjit WassanUnderwhelming story... Why doesn't the BBC cover zero point energy sources such as Stan Mayer's Water Fuel Cell or the Folks in Australia that are driving around their cars running on water. Modern Science is stuffy ans arrogant. If it drudgery then employ it. Maybe the world would be a better status if they did not absorb to reckon on Oil! BBC - Bring us HHO gas stories!!

Rick SpivillAnother triumph from the University of Reading's comp sci dept.

Mahesh SooriarachchiI contemplate this is just re-naming the problem to something else... then again, if you really contemplate about the basics of division, the problem of division by zero comes into being because of the thought that zero is not really zero, but a really, really little number. So maybe the solution this problem should be to define zero as being trually zero (ZERO), nothing, zilch, nada! Now if you examine at division this way, lets sigh you absorb an apple (thinking of Newton) to be divided among 2 people... each gets half. Now if you divide the apple between ZERO people, what accomplish you get? I beleive its the all apple... so dividing by honest zero is the number itself!

Jon BakerProving that NULL exists and giving a cutesy name. Now why did I not waste my time doing that??

UndanI was wondering... what would be the result of nullity/nullity ?

Kurt FitznerThe "problem" of a computer with divide-by-zero errors is not a problem, it's a feature. It's not something you need to or even want to fix. You could easily design a computer that doesn't absorb an error in that situation if that's what you want. Replacing the error condition with a fresh symbol accomplishes nothing. The program soundless has to deal with the issue in order to present a real-world result to the user. A divide-by-zero error is the pass programs accomplish that. It's simple to unravel a "problem" when you're the architect of the definition of the problem in the first case. Dr. Anderson first defines a problem: calculators and computers throw an error when you try to divice by zero, and then defines an ersatz solution - but the problem was ersatz in the first place. We've sum rush into poorly designed programs that don't handle divide-by-zero errors properly and crash. This isn't a problem of dividing by zero, this is a problem of a computer program not handling its data properly. We've besides sum rush into programs that attempt to reference a null pointer. By the same reasoning, they could define the reminiscence that a "null pointer" points to as some fresh sort of virtual space called "nullspace" (trekies should esteem my resistance to the temptation to convoke it "subspace"), and convoke it valid. fabricate the computer such that reading from "nullspace" always returns a null. Suddenly no programs crash from dereferencing a null pointer any more. It doesn't stand for that the program is going to now accomplish something useful. It probably means it will discontinuance up displaying garbage to the user, hanging in an illimitable loop, or branching off to never never land. As far as it goes mathematically, there's nothing you can accomplish with nullity on paper that you can't accomplish by simply leaving it as (0/0) in the equation. So from either approach (mathematically or from a computer science perspective), it's nonsense. The author's own response to some of the critics (or, I should say, alleged response) doesn't aid my opinion. Tossing out the names of two other Ph.Ds and offering vague references to undescribed "axioms" built around this fresh symbol sum reinforce my sentiment that Doctor Anderson sounds precisely enjoy the character Robert from the movie "Proof".

SteingrimHe's worked his pass in an apparantly conventional manner to where 0/0 = 0^0 Okay. Then he assigns "nullity" to both sides. So what ?

ShadowkillerSo wait, let me contemplate if I understand here. Nullity = 0/0. As the professor showed us, 0=1+(-1). So 0/0 = (1+(-1))/0 = (1/0)+(-1/0) = Infinity + Negative Infinity. As everyone knows, anything minus itself equals 0. So this means Nullity = 0. accomplish I win a prize?

JasterSo Dr Anderson replies motto he IS using 1/0 = infinity which is erroneous (1/x tends to infinity as x tends to 0, but this does not stand for 1/0 = infinity) If he defines Nullity = 0/0 and Nullity does not aid with x/0 problems on computers (testing for division by zero is already done and testing for nullity is as easy) then what employ is it ... this does not explain that and neither does his reply on this forum This might be relevant and useful but not to computer science - computers already cope quite well enough ... but what does it allow you to do? this has not been explained?

keshi just read anderson's post. he seems to be using the true projective line and then motto 0/0 is not on the true projective line. and this gets published as original?

BrianIf a computer program divides by zero and crashes, that is not the computer's fault, it's the programmer's fault. It's throwing an exception, and if you don't entrap the exception, then you're not a very safe programmer. This PhD didn't listen very well in his first year CS course.

fellow anonwow, anon really left alot of messages tearing this guy apart. i wanted to respond to some below comments, but there is no >>1748433373 to click on. However this is /0 GET.

2+2=22This is totally incredible I adore you man =)

Darren McDonaldThis is nonsense, nothing has been solved. Your mediocre maths A-Level student would be able contemplate that. The BBC should feel ashamed for publishing this.

ijif "Let me try to answer..." is really by that "Dr James Anderson", I just can't understand he can train somewhere. The only thing I enjoy here is the "General error has occurred" message (Dr Anderson's theory in detail).

EverettI abominate to add to the slew of comments, but I can't desist myself. You can't accomplish this to the true line and preserve it's properties. At the fundamental topological level, positive infinity and negative infinity aren't on the gauge number line - it doesn't absorb upper or lower bounds. And if you tack on another point "outside" of it, you change the topology. Is that point an open set? Closed? 0/0 isn't a problem that can be "fixed". It's a property of the true line.

DavideLHmmm ...: Inf = 1 / 0 Inf * 0 = 1 [A] Inf * 0 = (1 / 0) * 0 Inf * 0 = (1 / 0) * (0 / 1) Inf * 0 = 0 / 0 Inf * 0 = Nlty [B] By [A] and [B]: Nlty = 1

AyeRoxorNullity is merely a symbol that says "I don't know". Not quite as groundbreaking as it's being made out...

JimMy god that does it P=NP ... it's finally proven.

PatrickNullity may unravel the problem of writing 0/0 as 0/0, but doesn't unravel the universal problem of dividing by zero. What they need is a fresh sign, not a fresh number. examine at it this way, if you divide 23 by 0 and Get nullity, try multiplying nullity by zero. accomplish you Get 23 back? No! What accomplish you Get back? Another nullity? Zero? Where's my 23? Now respect a fresh sign: '@'. 23/0=@23 -23/0=-@23 @23*0=23 -@23*0=-23 Start looking in the second dimension and contemplate the number line is not ---, it's -|-

Dr of what?Simple proof that breaks "nullity": y = y y2 = y*y (y-y)(y+y) = y(y-y) Φ(y+y) = Φy [divide by zero] Φy + Φy = Φy 2(Φy) = Φy 2=1... ?

Mark SkerrittIf you absorb 0/0, its undefined, employ calculus to Get the desired result. This is useless.

chrisI don't know where you guys absorb been sum these years, but math did not just drop into their laps fully formed. It's always been about defining systems that are governed by rules (axioms). As long as your system is internally consistent it is valid. (There are non-Euclidean geometries where triangles can be made from three 90° angles.) Now some consistent systems are more useful than others; if it is honest that Dr. Anderson's system contains the all of gauge arithmetic along with this fresh definition, then I contemplate no problem with it. I would be interested in seeing sum of the axioms defined. recollect that for a long time everyone thought 1/0 was impossible to define, but now it is accepted that 1/0 = infinity. This fresh concept is really not much of a stretch beyond that.

vrochelet me guess, next someone is going to arrive out with an 'everything number', if it doesnt exist already, that contains every number [read:every state]. Schroeder's Cat = 'everything'

navim88...really....? step 1. people don't know the reply to a problem step 2. ill designation the problem "nullity" step 3. the reply to the problem is "nullity" wow I'm smart.

Martin SpamerI'm a Computer Scientist not a Mathematician and a natural sceptic. However this is entertaining because of the symmetry with how null IS handled in Software Enginnering. Null != 0 and is held outside the scale of true numbers. Null is usually represented as \0 which might present a better alternative than a fresh symbol.

WillAll he's done is fabricate a designation for a problem to mask the problem... I don't contemplate it really solves anything.

Kirill A. WoroshilovAnd what does that guy contemplate about L'Hospital's Rule?

Emmanuel D.I am very sceptical about such "theory". First, it is quite confusing, and I don't contemplate how it can aid to understand some problem. if 1*nullity = 2*nullity, then nullity/nullity = 1/2 AND nullity/nullity = 2/1. But even worse, 1 = 2*nullity/nullity. So you absorb to sigh that nullity/nullity is undefined to explain this answer. Your transreal arithmetic fails to accomplish this, as far as I understood it. Second, since it's soundless confusing, Iit would absorb been better to wait for for mathematical evidence before teaching this eccentric things to pupils. This is nearly criminal. Next year some other teacher will arrive with a theory that says that 2+2 can be equal to 5 for very large values of 2 and little values of 5. Will he be birthright to train this to pupils before being confronted to his collegues? I contemplate no. Working in this pass is just plain dangerous. Science and math needs to be proven before they are taught - that's a basic fact. You besides failed to accomplish this, and this is criminal imho. Finally, nullity doesn't really aid when it comes to computers. How will you picture it (and both infinity and negative infinity) using a 32 bits integer? Or a 64 bit integer for that matter? recollect you soundless absorb to succeed the rules of 2-complement arithmetic... That's going to be quite hard. I guess the solution is to give them some special values, and to hardwire the calculus in the ALU - this is not very efficient imo. I don't want to sigh that the theory is some random bullshit (I'm inclined to contemplate that a representation of these numbers is quite important), but I'd wait for better proofs - ie not proofs that are backed up with the IEEE FP standard.

SkuffIm no mathmatician (infact i struggle to spell it). So im not really positive about sum this 0 stuff. But i contemplate the reason math exists is to drudgery things out, probably starting at some local shop and adding beads or something etc...il trade one loaf for two fo these or what ever. So in my ignorance I examine at it simply, such as: sigh they absorb One cake. They absorb 5 people. The cake weight 500g. So each person (if divided equally) gets 100g of cake each. So, if theres 1 person, they Get the all cake, 500g. So, if there arent any people to divide the cake between, doesn't that stand for that 500g is soundless left? Crude, Im sure. But, surely thats right? 500/0 = 500? I guess this might be fraction of the problem, in maths this just cant work. I accomplish find that there seems to be a few holes in the cavity mathematical system and they appear hell bent on trying to withhold it as the birthright pass to accomplish things. Its takes someone to try and prove other systems, it seems in todays world they materialize delighted to employ old(ish, perhaps, although improved over time) methods that yes, absorb been tried and tested, but may be not entirely correct. If a tree falls in a wood and no ones heres it, does it fabricate a sound. Yes, of course it does, dont request such daft questions ;)

YabaTheWhatThere is absolutely no need for this imaginary value. First off, any number to the power of zero is one. Why? Let's sigh N is a number, and R is some random number. RxN^0 is interpreted as, "Multiply R by N zero times," or more generally, "Multiply R by... wait, no, nevermind, just leave R alone." Next, let's address the concept of 0/0, or zero divided by itself. The simplest reply is that any number divided by itself is one. Obviously computers absorb a problem with this concept, so let's approach it from a more all-around standpoint. Computers absorb difficulty dividing by zero, because 1/0 is infinite, and computers only deal with finite numbers. That's the problem designers would need to fix. Instead of treating numbers as finite values, tack on an infinity tracker. Let's employ oo to picture infinity, since I'm writing in a text box. The basic problem is that 1/0 = oo. In finite mathematics, that causes an error. However, 1 in a finite system is actually 1 not multiplied by any infinites (or not divided by zero). They could sigh that finite 1 is 1 multiplied by no infinites, or "one with zero infinites" as a shorthand version. Now divide it by zero. The result is one with one infinite. Now divide 1 by this result, and you Get 1 (from 1/1=1) with -1 infinites (1/oo). Divide this number by zero, or multiply it by oo, and you're back to 1 with 0 infinites, or finite 1. To divide by zero at any time implies that zero is, in fact, not an absolute value, but simply an infinitesimal value; it is so little that it is regarded as nothing. This, from the perspective above, would be called, "one with negative one infinites." They could, of course, multiply it by itself to Get the value, "one with negative two infinites." Multiply this by oo, or one with one infinite, and you're back to one with negative one infinites. Multiply by oo again, and you're at one with no infinites, or finite 1. Taking the concept a step further, respect the simple equation (x^2)-(2x)+1=(y^2). In finite math, that's a simple problem to resolve. What about if x = oo? The reply is that it's soundless the exact same problem. The answer, y=x-1, soundless applies. Writing out the equations, we'd absorb one with two infinites minus two with one illimitable plus one with zero infinites equals the square of "y", resolving to "y" equals 1 with one illimitable minus 1 with no infinites. So what's oo^oo? Guess you'd need to tack on a second infinity counter to the number at that point. While I wouldn't hope a simple hand calculator to handle this problem, any scientific calculator designed to handle the square root of negative one should be able to handle infinites in this manner. Getting back to the all issue of "nullity", it's basically useless. Nullity basically means, "One multiplied by some finite numbers I was too distracted to track." If accepted by the mathematical community, it could easily be used to prove that 1=2, or a variety of other nonsense. [Gyeh. There are too many replies to this discussion already. condone me if someone has already said what I just said. It always seemed to me enjoy a fairly obvious solution.]

AnonI'm studying in the Reading University Mathematics department. I would enjoy to point out that this guy is not a mathematician and works in the computer science department. Hence any theories that he proposes are nothing to accomplish with the mathematics department.

David MellorWhy such skepticism? I'll wager people would absorb said the same about the square root of minus one, and examine how useful that is now (really!).

BlackTiger... Quite strange. If you are dividing something by 4 it means "divide in 4 pieces", isn't it? Ok. What is result of "dividing in 0 pieces"? Just nothing. What's wrong with it?

DecipherInventing a fresh term to deal with it, is not really solving it, is it?

AimeeTry a different symbol, sir! That one your using equals 1.618 and it's one of my favourite numbers!

MaryMy understanding of the true numbers is that they don't actually end. So how can infinity absorb a value? That would stand for the discontinuance of the true numbers, which is not possible.

NullityI absorb nothing to say.

Albert EinsteinWhat is nullity divided by nullity? Negative infinullity?

ConfusedIf this problem hasn't been solved for 1200 years, who solved it 1200 years ago?

PythagorasIf the definition of infinity (positive) is 1/0 then is 2/0 not two times infinity? This would be a larger infinity by the math rules that I know. This concept can be extracted an infinitum. As a result, 1/0(1/0) is an illimitable infinity, besides know as an absurdity. Does this fabricate any sense? Infinity is illimitable by definition and therefore nothing is larger. Maybe, just maybe Mr. Anderson is 1/0 nuts. That's it, the man is off his blinking rocker. Now for there true issues of life - just how many angels can felicitous on the head of a pin?

D.V.1. if you read his axioms you will realise that "nullity" is what humans absorb been calling "undefined" for 1200 years. The axioms are identical. He just renamed the word. 2. if your heart pacemaker divides by zero you are NOT dead. there are things called watchdog timers that reset microcontrollers when things enjoy that happen. 3. creating an remonstrate out of "undefined", called "nullity", that behaves identically to what they absorb always known as "undefined", does not aid computers or mathematics any.

KhojiDr James Anderson wrote: "It is just an arithmetical fact that 1/0 is the biggest number there is. " Rubbish. That's about as meaningful as motto that an orange divided by an apple is a pear. 1 is a quantity. 0 is the lack of a quantity. Using symbols from the same numerical system for both of them creates the intellectual illusion that they are both numbers, but they are not. Thus, the entire nullity edifice collapses upon itself.

Beender DundatMy theorem: any number (includig zero) devided by itself is 1, ex. 1/1=1, 123/123=1 and 0/0 = 1 and infinity/infinity = 1. Also, any number (including zero) to the power of 0 is 1. Anything devided by zero is infinity (positive or negative, depending on its sign). immaculate and simple.

UnnessecaryStudentEhhmm... Thats eccentric - To declare a fresh "number"/"letter". I'm not delighted about this solution. I'm sorry.

JaapHi, If this problem is 1200 year old, then what does Pythagoras absorb to accomplish with it?? And as physicist I did not contemplate any fresh math here.

AnonymousAny Java programmer will be able to contemplate the similarity to Double.NaN (Not a Number) constant. This was introduced by Sun atleast in 1996, could absorb been earlier if done in other programming languages too. The only extension here seems to be that its being brought into the non-programmer world.

Brian MatthewsHere's why 'nullity' doesn't work: WHat is nullity divided by nullity? Well, it's 1, isn't it? On the other hand, this is besides equal to (0/0)/(0/0), which by simple maipulation of fractions is equal to 0/0, which is nullity. So nullity equal 1. Nonsense. QED.

SekkyGuys, this legend is in no pass analogous to complex numbers. complex numbers are no more or less artifical than the negative integers or rational numbers, they're sum just extensions to provide a superset. They are in no pass enjoy what is being suggested here, which by the way, is an embaressing regurgitation of absolutely nothing. Ignore sum research papers from the University of Reading.

Navid ZamaniI KNEW it! I KNEW it the all TIME! Never since i first heard that there is an "exception" to sum math, when using zero, i felt very stalwart that this is wrong. enjoy a glitch in the matrix or 2+2=5... You know it. I searched for solutions to it. But they mostly went with "something / zero = infinity_n" where n held the information about "something", so by muliplicating "infinity_n * zero" you would Get "something" back. Worked quite well, but there were problems with it.... (that i can't recollect for now) I'm REALLY delighted this happened! So i finally can relate my ex-teachers that *I* were birthright sum the time! THANK YOU MR.... Anderson...? Oh... my.... GOD... I's you Neo! You solved the glitches! :D

MikaelSo, how does this relate to the theory of algebraic wheels; which as I recollect it besides deal with 0/0 by extending the extended reals to involve this as a fresh formal element?

Three lofty School Math Teachers Mr. Gagliardo, Mr.This is not something fresh under the sun. 0/0 is undefined; but it can be besides be considered indeterminant because it can be any value. 0/0 could, for example, be 7 because 7 x 0 = 0. It could besides be -41, .2, etc. Calling it nullity is just a bit too cute. However it gave us something to contemplate about.

Kyle BurtonI'm sorry, but there isn't exception handling in integer division

Funny ThatThis has to be a crack of some sort! Some distinguished comments below though: Bob:"The program wont crash, but the plane positive as hell will." :0)

Dr Richard Daniel HillThis man is a charlatan and a crank

ライト0/0 = Nullity? Next thing they know, he will relate us that .9~ =/= 1.

nullity.complex: defn: people with nothing to accomplish bIt does amaze me that so many smart people feel the need to shoot down another mans ideas....whether despicable or good. Obviously shrimp else to accomplish with their null lives. Its simple to be a critic. And nearly every commentator has arrive up with the solution at some stage in their puerile lives. One things missing...why did these people accomplish nothing with their fresh ideas? Even distinguished minds had solved problems in the past, but gained no recognition for it because one has to contemplate opportunity/value in such solutions. From my point of view: if i seize 10/5 = 2 and convert it to 5*2 = 10 then I would hope that 1/0 = ? could be rewritten as 0*? = 1 but multiply by 0 gives you 0. This is what we've always been thought. They can besides never relate if 1/0 is negative infinity or positive infinity yet both are possible. NULL is used in computer programming to define stand for nothing/empty/undefined. Its allows checking for the actuality of something of interest. Comes from the latin word nullus meaning "not any" Is it not workable the professor is trying to explain this theory through algebra..... I cannot view the video so I accomplish not know. And so what if its been discovered. I'm positive its a helpful approach to teaching this stuff.

JCAI prodigy how Dr. Anderson handles (a true number)+(infinity) - (another number)-(infinity). Since his infinity lies where it does, how does he handle it?

prober8if: 0/0 = Ø so: 0/Ø = 0 then: Ø = 1 ??? nullity = solidarity ???

Adam BraunExpress it as binary.

AnonEvery field has a nullity. That's basic abstract algebra. One should be wary of people defining things conveniently without rationale or proof - what you've got there is just numerical masturbation. Avoid mathematical sensationalism at sum costs!

MattI came up with the same solution years ago except I used the symbol "Doh!".

Thom HowesSimple question, if the numerator and the denominator both approached 0 at the same rate, wouldn't the result always be 1?

SimonIt's honest that dividing by zero does antecedent an error in programing, but any programer that has every written a program more complex than "Hello World" (Tradtionally the first program you ever write), will know to trap the error before it occurs. So it can be dealt with gracfully (i.e. assigning a defaul value instead), rather than crashing. Any of the modern or remonstrate orientated programing language will absorb expection handling built into the it for just this sort of problem. As a computer scientist, I would absorb hoped Dr Anderson would know better.

Mutant RobSo has he vetted this thought in reputable maths journals among other mathematicians, or is he using his power as a school teacher to foist quack ideas on his students, much enjoy "rational trigonometry"?

ChrisNewton? Fool. Pythagoras? Useless. Anderson? God. ingest your heart out, creators of mathematics as they know it!

The MoleSo: Ships and planes unexplainedly evanesce in the Atlantic. Let's assume there's a location which lies outside the gauge space/time line and give it a name. Now the disappearances are sum explained just by motto "Bermuda Triangle".

LJLIt's been a long time since my Advanced Theory classes, but doesn't a number lying OFF the number line violate the axiom of Completeness? I find it difficult to believe Dr Anderson would absorb simply overlooked the most basic axiom in advanced mathematics, but that's exactly what he appears to be doing. Before contradicting the employ of the term number here, let's puss it, anything used to picture a value is a number, even if you convoke it a non-number. I absorb a problem wrapping my brain around a value divided by a value producing a non-value. One might as well sigh 6+10 = a dog. This is violating - or rewriting if you prefer - a number of concepts that the vast majority of mathematics, from simple computation to advanced theory - relies on. I won't retreat so far as to employ the derogatory terms presented by other commenters, but I certainly contemplate dropping this from the drawing board to a schoolroom without peer review and universal acceptance is irresponsible at the least. I accomplish realize that the particular problem of division by zero is a particularly anomalous one, so I can understand the unorthodox approach, but there are times when either infinity, negative infinity, zero, or 1 minister to "fit" human intuition - which they sum know is not always even close, but for real! I accomplish contemplate there's a pass to handle this, but I contemplate it's maybe just a shrimp more involved than "Hey! Let's fabricate up a fresh (non)number!"

GooseAnyone know of a credit card with this kindhearted of interest rate??

No bodyTake the pairs (a,b) of true numbers. Two pairs (a,b) and (c,d) are "equivalent" if there exists a non-zero true number x such that c=a*x and d=b*x. This is an equivalence relation. Let "a/b" denote the class of (a,b). Let the "product" of "a/b" and "c/d" be defined as the class of (a*c, b*d). Let "nullity" be the class of (0,0). Is there something more in the nullity theory?

Mark JohnsonCan they invent some fresh letters to the alphabet as well. Sorry but "making up" a fresh number does not unravel divide by 0. The reply should arrive out as an error and thats the pass it should stay.

its meI too absorb solved an traditional age problem. The meaning of life which I convoke Liath. It is quite simple now that they understand that Liath happens between Life and Death ;)

Nathan GerberSo ok if this is solved, just how accomplish I seize this fresh value and continue solving a problem? Basically sum this is doing is taking away a "divide by zero" error and replacing it with a "nullity" or "negative infinity to positive infinity" error.

QrizWow...some loooooong explanations there. 0 is something they made up. dividing by 0 (for example, dividing 9 into groups of 0) would Get you infinity. So you start dealing with kinds of infinity, which is besides a concept, not a definable value. Zero and infinity are artificial, and they aid us picture and drudgery through problems. enjoy someone said down there, math is sum definition. There isn't a "right" reply unless it fits these definitions.

DaveHyperbole. I had to present more proof in grade 5 - but I suspect this quack has no proof.

Stephen Leary0/0 is Not A Number. This is well defined in computing science/Maths etc. "Nullity" is just a redefinition of this and has been around for years.

CharlesNice joke. But you can't reclaim a quantity on Nothing, that should be just about Obvious to everyone around here

Carolus HolmanIf I seize an Orange, and divide it by Noting or 0 or don't lop it, I soundless absorb a all orange. So in my layman brain 1 orange divided by nothing is soundless an orange. I am surprised that the British are so gullible, but then again, I am British.

JoeDr Anderson has done nothing but add a fresh notation that was not needed. His definition of 1/0 as Omega is flawed, as there are larger illimitable numbers. Modern computer programmers employ exception handling to manage the "divide by zero" error, and this "new" concept adds nothing to that science.

Cracked out winoDude, Nullity RULZ!!!!1111@#$ Professor smart guy for preZ!

Stuart difficult ManThis guy needs to toughen up. Seriously Plus Lee and Bag accomplish some work!

Story ProblemThere are twenty apples in a bag. Neither Rick, Jane, Sam or Betty want any of the apples. How many apples does each person get? 20/0 = nullity Each person gets nullity apples.

Bored of EducationSorry, this guy is a fool. Nullity is not a true number, and you cannot achieve it from dividing by zero BECAUSE YOU CANNOT EVER DIVIDE BY ZERO TO commence WITH!!!

ummmummm true player? are you serious?

MikeThis is just stupid, nothing has changed, they just now absorb a designation for the no non-value that results. You may as well convoke it error so that at least the calculators are soundless right

C R HulcherZero is a status holder, never was a "number"!!!!!

JoeThis is not unlike astrophysicists who, when their numbers don't work, just theorized something they convoke "dark matter" which does nothing but fill in the gaps in their equations.

ChocoSo many comments here from the computer programmers' camp - how many of you can honestly sigh the computer languages from which you draw your examples are mathematically rigorous? When was the terminal time a mathematics prof wrote "Type mismatch" on the blackboard? A bit of reading up on e.g. Peano arithmetic is needed before challenging Dr Anderson's working.

de GraafSo... does this succumb an reply for the Le=orentz-Fitzgerald equation (that yields a division by zero when the velocity of an remonstrate matches that of light)?

TofuHmmm.... I absorb an insolvable problem. I KNOW! I'll just fabricate up a brand fresh irrational expression and title that that is the answer! His step-by-step "detailed" illustration doesn't unravel 0/0. He just gives a convenient placeholder instead of an error message. besides how can he convoke "nullity" a number if it doesn't Fall on the number line? Heck I could sigh an apple is a number now and employ his same logic to validate my theorem.

Gunnar GregerDivide infinity by infinity: Infinity/infinity=0, or is it? contemplate about it. 0/0=Infinity or is it 1? The solutiuon is hidden in infinity?

Peter Tettweiler, Hamburg, Germanyto be honest: no!

Shady TarekIs there any practical problems solved with this ? I stand for ok there's a fresh number now what does it accomplish !

Matt FletcherExtending the field of number by adding special elements (e.g. infinity) is a basic and picayune operation in alegbra. There is absolutely nothing fresh here at all. The BBC should only report scientific advances published in peer-reviewed journals. Anderson's drudgery seems only to be released via his personal webpage where his paper supposedly demonstrates "the possibility of division by zero and challenges the reader to accept it". Not the habitual wording for a technical paper with something genuine to say. gratify desist giving this nut free publicity.

DavidJust accomplish what I accomplish - when in doubt what accomplish you Get if you multiple 6 by 9? 42. (And for those who don't contemplate the connection - 6*9(base 13) does indeed equal 42 :) Thank you to the late distinguished Douglas Admas for that Gem. 1/0 or 0/0 will remain NaN for a long time yet. Until C supports nullity - no computer will stand a casual of understanding the concept at the basic operating system level.

Alexander RozmanHow does making up a fresh symbol unravel the problem of computers diving by zero? Just how does this theory suggest encoding nullity in binary or performing arithmetic operation on it?

TRexThis is great, but I don't Get it, can you write a job aid for it?

Morten V ChristiansenI am not positive what Dr. Anderson has done, but in principle the thought is not problematical. Several non-standard interpretations of number theory exist, some with illimitable sets of "alternate zeroes" or infinitissimals. They are provably as consistent as gauge number theory. This is no different from non-standard set theory or non-euclidian geometry. If Dr. Anderson has created an proved the consistency of such a system, which is accessible enough to be understood by school children, I contemplate that is a very nice accomplishment. It does not revolutionize mathematics, but it is very nice work.

AlphaAXPThis theory looks itself a lot enjoy the own result it referes to: a nulity. "A" quantity, even if abstract, can be defined, not "Any" quantity. amusement but not original. math already owns a symbol for "Any value": it's a capital "A"O upside down.

Dr. OH RLY ObviousTo: Dr. Obvious, If you times a irrational number a rational, you Get a irrational.

RouDyThe 2nd step before the latest is erroneous (1/0 is impossible). And 0/0 is impossible too. (sorry for my despicable english, i'm french)

Tim PozzaWill the fresh number allow us to calculate when infinity touches itself in space and in time?

ZipNot a Number is basically enjoy a workaround to withhold an application from crashing a virtual software engine. That's about it. It's not a mathematical proof of anything. Basically, sum he did is to propound a routine that can be used in divide by zero situations, that's it. There's no reason for almost sum of these chest thumping replies. It is true, though, that this probably isn't going to magically fix software glitches of any kindhearted in modern managed code. Maybe it would allow lower smooth code (assembler, c, etc.) to not absorb to entrap divide by zero errors on systems with updated firmware that handles the concept of "nullity". That's about it though. The problem then becomes backward compatibility. ;)

Michael ClaytonQuoting the Dr. Anderson "It is just an arithmetical fact that 1/0 is the biggest number there is.". That is plain RUBBISH. Patently FALSE. Here's the proof: 2/0 > 1/0

SebHaving 0/0 as undefined is useful as you can't employ it. If you define it as a symbol people employ it in algebra and you discontinuance up in sum kinds of 1=2 kinds of problems, throwing out an error from your calculator is a safe badge you made a mistake and should retreat back and fix it.

JMSI'm relieved to contemplate that his PhD wasn't in mathematics. That said, the respect that the title "Doctor" brings should be used wisely, and certainly not in misinforming the universal public, let solitary vulnerable children. This made me very mad indeed, to sigh the least. Angrier still, when I read his papers on "transreal analysis". Again, I'm joyous that these won't be published in any respectable mathematical journals. What he has done is not mathematics; it is more closely related to the field of linguistics: don't absorb a word for something? Let's fabricate one up and then employ it to explain the same word. He has decided that the problem of dividing by zero can be solved by motto that if it could be solved, its reply would be "nullity". Ignoring the fact that nullity then breaks most commutative laws, he has not used nullity as a routine for solving any true problems. Some absorb said that his "work" is analogous to the discovery of the imaginary number i (the square root of -1). However, i is useful in solving many mathematical and real-world problems; nullity certainly is not. His papers title to invent a fresh shape of arithmetic that allows the employ of his fresh number, but in reality they simply add axioms to the existing set so that he gets around the problems thrown up by nullity. Furthermore, he envisages the computers of the future using his fresh shape of arithmetic so that the "NaN" error is replaced by "nullity". How does that unravel the problem? Even if the computer then knows how to employ it in equations, it won't give any reasonable answers since, by his own calculations, any equation involving nullity has an illimitable number of solutions. How dare he masquerade as a mathematician? How dare he waste valuable research grants on a something so useless: something that, unlike honest mathematics, has no scientific, philosophical or practical value? I am delighted to contemplate that there are an overwhelming number of comments on this page ridiculing his drudgery - most of these people probably absorb less education than he but they can easily spot the fallacies in his utterly ludicrous, crackpot theory.

cies breijs"-Inf" and "Inf" are no numbers, so "Nullity" is not a number ("NaN") aswell. They could fabricate a contrast between different "NaN"'s and convoke them "-Inf", "Inf" and "Nullity", but will this fabricate sense? They they be able to accomplish somehtings that was previously undoable (like complex numbers enable us to do)? I don't contemplate so: NaN + 1 = NaN NaN * 2 = NaN this hold honest for any NaN, so this renders them useless.

WalemfrickGreat work! If nullity extends from negative infinity through zero to positive infinity then it is a sound reply for any problem not just this one! 1+4 = NULLITY!, the root of 123786476362783456734 = NULLITY! If this gets accepted nobody has an excuse for scoring less than 100% in Mathematics ever again, sorry NULLITY%.

All this is very usefullPerspex machine: VII. The universal perspex machine James A. D. W. Anderson The Univ. of Reading (United Kingdom) (published online Jan. 15, 2006) The perspex machine arose from the unification of projective geometry with the Turing machine. It uses a total arithmetic, called transreal arithmetic, that contains true arithmetic and allows division by zero. Transreal arithmetic is redefined here. The fresh arithmetic has both a positive and a negative infinity which equivocate at the extremes of the number line, and a number nullity that lies off the number line. They prove that nullity, 0/0, is a number. Hence a number may absorb one of four signs: negative, zero, positive, or nullity. It is, therefore, impossible to encode the badge of a number in one bit, as floating-point arithmetic attempts to do, resulting in the difficulty of having both positive and negative zeros and NaNs. Transrational arithmetic is consistent with Cantor arithmetic. In an extension to true arithmetic, the product of zero, an infinity, or nullity with its reciprocal is nullity, not unity. This avoids the habitual contradictions that succeed from allowing division by zero. Transreal arithmetic has a fixed algebraic structure and does not admit options as IEEE, floating-point arithmetic does. Most significantly, nullity has a simple semantics that is related to zero. Zero means "no value" and nullity means "no information." They wrangle that nullity is as useful to a manufactured computer as zero is to a human computer. The perspex machine is intended to offer one solution to the mind-body problem by showing how the computable aspects of humor and, perhaps, the all of humor relates to the geometrical aspects of corpse and, perhaps, the all of body. They review some of Turing's writings and present that he held the view that his machine has spatial properties. In particular, that it has the property of being a 7D lattice of compact spaces. Thus, they read Turing as believing that his machine relates computation to geometrical bodies. They simplify the perspex machine by substituting an augmented Euclidean geometry for projective geometry. This leads to a general-linear perspex-machine which is very much easier to program than the original perspex-machine. They then present how to map the all of perspex space into a unit cube. This allows us to construct a fractal of perspex machines with the cardinality of a real-numbered line or space. This fractal is the universal perspex machine. It can solve, in unit time, the halting problem for itself and for sum perspex machines instantiated in real-numbered space, including sum Turing machines. They cite an experiment that has been proposed to test the physical reality of the perspex machine's model of time, but they fabricate no title that the physical universe works this pass or that it has the cardinality of the perspex machine. They leave it that the perspex machine provides an upper bound on the computational properties of physical things, including manufactured computers and biological organisms, that absorb a cardinality no greater than the real-number line. ©2006 COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal employ only.

MattTo me, it looks enjoy the reply is soundless the same as it has been for the past 1200 years, he's just decided to draw a squiggle at the discontinuance claiming its the symbol for 'nullity'

Gunnar GregerDivide infinity with infinity:infinity/infinity=0 or is it zero?Think about it.

Richard Bremner, Aberdeen*Announcement* I absorb solved the problem of what is North of the North Pole, it's called Northity. Everyone rejoince.

mikeWasn't this article prepared for 04.01.2007 ?

Michael McGuireThe man is a crank on the smooth of the "squaring the circle" crowd. The accepted value of 0/0 is undefined for several safe reasons that anyone with an understanding of topology or even basic calculus should understand. Replacing 0/0 with a special symbol would actually create more problems than it would fix. I recommend a quick examine into the works of Cantor and/or Komologorov for anyone who is interested into modern theories of zero and infinity.

Wayne SmallmanAm I the only one to totally underwealmed by this fresh theory of nothingness? If sum he's doing is making up a fresh non-number, I'm hardly surprised by him solving this problem. Almost any problem can be solved by just making stuff up to felicitous the problem. Some peer review might be more telling...

HONKHURFEY DURFEY baby, congrats on coming up with a cute fresh designation for an already proven concept. There isn't anything fresh here except a silly designation and a washed up professor.

Dr James AndersonLet me try to reply the comments posted above. I absorb defined a fresh number, nullity = 0/0. I used a symbol, capital phi, to denote that number. The symbol I employ is irrelevant, what matters is the definition of the number. I’ll sigh a bit more about this number in a moment, but first let’s Get limpid what they are talking about. I besides defined infinity as 1/0 and minus infinity as -1/0. This is consistent with dividing a non-zero number by ever smaller numbers approaching zero. The geometry of this arrangement is shown in the video. The number line stretches from minus infinity to plus infinity. It does not wrap around into a loop, it does not identify positive and negative infinities as antithetical poles in a projective geometry (though it is workable to accomplish that if you want to). The geometry is exactly as shown in the video. The number line stretches sum the pass from minus infinity to plus infinity in a straight line. The fresh number, nullity, lies off the number line. I drew it above zero, but it can be drawn anywhere that is not on the line. Its geometry can be understood in the same pass that the number i, the square root of minus one, can be understood. sum of its algebraic properties can be drawn as pictures in co-ordinate geometry. Some people employ j to indicate the square root of minus one. The symbol does not matter, what matters is the definition of the number. Once I understood the geometrical picture of the fresh numbers and understood how to operate on them as fractions, using pencil and paper methods, I wrote the all lot down as analytic rules or axioms. Dr. Andrew Adams from Reading University and Dr Norbert Voelker from Essex University helped me develop the axioms. Norbert translated the axioms into higher order logic and used a computer to prove that they are consistent. The axioms contain the all of gauge arithmetic. This is very important, it means that anything that can be calculated using gauge mathematics can soundless be calculated, but now it is workable to calculate other things as well. I’ll sigh a bit more about this later, but birthright now let’s contemplate why nullity is a number. There are many ways to contemplate about numbers (and I employ whichever pass is convenient at the time), but one of the simplest is to sigh that a number is anything that obeys sum of the axioms of arithmetic. Therefore, nullity = 0/0, infinity = 1/0, and minus infinity = -1/0 are sum numbers because they obey sum of the axioms of my fresh arithmetic. I contemplate the world has settled on oo as a symbol for infinity, though aleph and omega are besides used for different kinds of infinity. If you want to rush a competition to find a better symbol than capital phi for nullity then retreat ahead. If it’s a nice symbol I will employ it in my scientific papers. In my axiomatisation it is defined that infinity is greater than zero. From this it follows that infinity is greater than sum numbers. I’ll reclaim a proof at the discontinuance of this message, but let’s be limpid on what this means. The property of being infinitely broad follows from the fact that a positive number is divided by zero. It is not necessary to define infinitely broad by any other means. It is not necessary to employ calculus or set theory to define infinitely big. It is not necessary to employ any philosophical concept of bigness. It is just an arithmetical fact that 1/0 is the biggest number there is. As I said, there are various kinds of infinity. It is workable to add these to the number line. They are sum smaller than 1/0. In some areas of mathematics a biggest infinity is defined according to the axioms of that area. Several areas of mathematics employ the symbol capital omega to denote the biggest infinity. Its properties depend on the axioms in employ so they can vary from district to district of mathematics. My infinity shares the property of being the biggest infinity, so you can employ capital omega as a symbol for it if you want to, but the properties of my biggest infinity succeed from the properties of my arithmetic and not from anything else. Some areas of mathematics define infinitely little num

Tormod HMath is sum about definition, and making consistent roules to succeed in every situation. to title that a conditional statement in computer code is fixing it; is just ignorance. with a math theorem defining how to handle this situations can help a lot. it is vital to understand that math is quite different than computer calculations; enjoy with diffenecials, it is workable to accomplish "calculations", but with constraints. if you rupture the constraints you outside conventional math and you are responible for you results. With a replete proven theorem around x/0 they can change computer science too. they just need CPU-core suport, and/or define som vector rooms. Major leaps in science history is done by changing the perseption, not claiming that they can cope with it as it is. enjoy the theroy of relativity. ( sorry for the spelling errors. Dyslectic, but not brainless :-)

MIchael ChizmarI could not open the video so I accomplish not know if this is relevant, but is there there a proof upon the definition of nullity? Or, is this just a rewording of what is already known, enjoy (a previous poster stated) NaN?

RenAwww I solved it years ago but didn't contemplate to publish it.. 1/0 = WTF? As you can see, my While honest Float is another word undefined, and the Float lets us know it's a fractional number.

Toshke from SerbiaThis is totally stupid enjoy sum similar proofs. Of course it didn't prove anything, he just created a fresh number, and same that number can be anything, from -inf to +inf. It is not going to aid any calculations. poverty-stricken children, at age of ten, they are being taught of infinity, they should accomplish it in lofty school. And this 'nullity' :( Forget it!

@ FredI conform how accomplish you repersent Nullity in binary or even hex. The other problem is he didnt even unravel the equation he just made up a fresh entity to provide a solution.. and nullity has always existed its called NULL so in essence he has just renamed the solution.

Dave GowerThis is, indeed, rather sad. 0/0 can be defined if a function that limits to it (such as sin(x)/x) is well defined and continuous. anything else, as mentioned above is simply NaN. They're not defined and probably never will be. The proof is diabolical. 0/0 = -0- therefore 0/0 = -0-. Yikes.

ytillunIf the airplane divides by zero, my pacemaker crashes :-) or, the pilot has to deal with "we are nullity meters from the ground. Press any key to crash now, or wait for nullity minutes for an auto-crash" How I wish my bank divided my $1 equilibrium by zero and told me that I absorb illimitable money ;-)

ComputingProfessorUm, this is nothing new. They absorb the concept of nan (not a number) and even accomplish arithmetic with it - any time one of the operands is nan, the result is nan. Fits nicely. So this is just a fresh designation for something that has been around for a while.

van de WeertIn my days as a student they talked about this same problem and defined a solution to it. They called that number "van de Weert", in reference to a much disliked teacher, they had loads of fun with it. And now this .... teacher tells his students this drunk ass talk of us is honest only using a different name? I convoke it cool, but I doubt any solemn mathematician is going to seize it seriously.

RobThe solution contains 0/1 x 1/0. But his definition states that 1/0 is positive infinity. So it's 0/1 x infinity. But they sum know that 0/1 = 0 and 0 x 'anything' = 0. So the solution is 0. Is it really necessary to 'make up' a fresh number? The verity is that he's trying to change the rules. 1/0 is NOT positive infinity! It is well understood that 1/0 is 'undefined'. I pity his students.

Brian K.Yes, at first i thought, "pretty cool", but after reading these comments, altho many are a lot meaner than they need to be, i accomplish contemplate now that no problem was really solved here. I mean, if you're depending on flight systems software, you're going to absorb to entrap a "nullity error" just as much as you would a "divide by zero" error. How would nullity propagate thru the rest of your algorithm??? explain that and maybe i'll revise my opinion.

Tasty WheatIf any number divided by zero equals nullity, then what does any number divided by nullity equals to? Divide by nullity error? :)

Blast RadiusThe IEEE gauge already defines 0/0 as NaN, which seems adequate enough. Nullity solves nothing and is simply an capricious designator that this professor invented. Unless "nullity" can be used in existing mathematical equations usefully, it is entirely useless. Bob has it revise when stating the uselessness of this non-number.

JohnComputers CAN divide by zero, if they employ IEE754 binary floating-point arithmetic (which practically every computer does). x/0 is positive infinity for positive x, negative infinity for negative x, and NaN (not a number) for 0/0.

Lumocolour O'ShaugnessyWill this fresh fangled contraption aid me Get a bigger slice of a shared pizza?

MikeI already solved this problem a long time ago. The reply is 0 AND whatever the numerator is. Where's my Nobel Prize?

CCMathematicians convoke that compactification of the true line, nothing new!

Ibzno prodigy i always flunked in maths!

a slightly less incompetent mathematicianTake a class on true analysis or measure theory. They construct algebras that can handle division by zero sum the time. Dr Anderson? This "new theory" is decades old. I erudite it as an undergrad, from professors who erudite it as undergrads. And it definitely isn't yours.

Dr DubeyActually, some unadulterated mathematicians had thought of thing quite some time ago (Sometime geometricts in the 19th century I believe).

freak guythis is crazy..if this is passed by the international community then let me propound a theory defining infinity upon infinity as "ellipsis"..

JDHe may be in the computer science department but he appears to be completely illiterate of modern safety critical software techniques. An auto pilot will not "stop working" if it tries to divide by zero, the software will entrap the condition and try to accomplish something sensible.

olLol! Thats just a nice joke! :-) Of course, the "nullity" number is known for a long time (it is usually called "undef") in most programming languages. The droll thing is to contemplate that people at the BBC buy this!!! :-)))

XpucmoWhat I find useful in his thought is that the fresh number could fabricate it easier and more gauge in programming languages to process results/events which are currently handled by exceptions. Plus it is always easier to employ a term "XYZ" than "the event which occurs when you accomplish this and this with that and that" - I contemplate this is called abstraction ;) Also, the very fact that this theory provokes such a furious reaction and polarized opinions means that it IS a fresh idea.

Ngrh8rWe absorb a designation for this "nullity" and absorb had such a designation for years. That designation is NaN. Learn it well, Anderson. You are no inventor, you are not heralding a brilliant and fresh mathematical theorem. You are simply giving a fresh designation to something folks from the computer camp absorb known for years.

noragree with u Caska might aid the computer programing and could be entertaining there.but for mathamatics not much aid lol

a uk college studentWhats this guy thinking? First of sum he thinks hes solved one of the most difficult problems ever, doesn't he contemplate that any mathmatician over the past however many years has thought 'hmmm lets just fabricate up a word for this and it'll sum retreat away' Honestly enjoy someone down the comments list has stated how is this to be represented in binary? I feel dreadfully sorry for the kids being taught this, many people in my previous math classes and I absorb said why not just fabricate up a word for it; it doesn't work!

Tomek PerlakWell, the concept itself seems appealing - it's just a fresh symbol. Just enjoy there isn't "really" an 'infinity' - there isn't "really" a 'nullity' - but it helps to explain something. (Does it?) I would kindly disagree with Hubert J. - IMHO, there is not really a mistake in this train of thought - please, notice that this fresh symbol is used to "simplify" the zero-to-the-power-of-zero expression. Merely that. Anyways - I'm kindhearted of a curious about some other expressions - can the 'nullity' be used in, say: -0- + 12 = ... ? -0- * 3 = ... ? Or are they talking here about a completely fresh set of numbers, almost enjoy with the complex numbers?

Johan Krüger-HaglertThis isn't news, and it absorb probably been solved long ago. Java for illustration sets a NaN-flag when you divide by zero, NaN standing for Not a Number. Afterwards you can easily check for such cases and handled them in whatever pass you contemplate is appropriate, the vital factor is that the program keeps on running instead of crashing.

!!!defining a fresh symbol doesnt fabricate up a theory

Prasob.kI don't contemplate this is possible.This concept of extended true line is already there in mathematics.ie "real line+negative infinity+positive infinity"...I don't understand what is novel about it!!!

BobbinsGreat, yet another headline-worthy pile of rubbish spouted by someone who clearly hasn't "got it". When will the press finally contemplate through this rubbish and desist printing such nonsense?

BadbarI had that theory for a long time but my anwser is 1. Because if you divide x with x you Get 1 as awnser. If you divide 0 with 0 you Get 1. If you contemplate enjoy dr anderson with the power system were 0 power to 0 is 1. That the anwser.

Jyri VedruWhat is here contrast from MATLAB language's symbol NaN (not-a-number)? MATLAB has been used it for a while.

Southampton ECS anonymousYou 'could' implement nullity using the "NaN" (not a number) feature of the IEEE floating point specification, having +ve illimitable as 2^149 and –ve illimitable as 2^-149. However, why not simply test your denominator before using it?

Ciaran Fowleythis cant be called a 'solution' as it just defined 0/0 as nullity, you convoke the artefact of dividing by zero nullity first, then obviously if you divide zero by zero you will Get nullity (which you just defined in the terminal sentance). you might as well convoke it peanuts, not nullity.

EnginerdLooks enjoy someone's trying to Get some undeserved fame. What a waste of my time watching that video and commenting on this so called theory. arrive up with something that matters in the true world...not these terrible examples about heart pacemakers and plane crashes. OK I'm done.

CrapolaI contemplate I'll retreat down Dr James Anderson's route and convoke the analytic result of the statement honest or erroneous 'Crapola' and thus absorb invented illimitable compression, give me a doctorate, professorship and a massive vouchsafe now!

Kim TherkildsenU must be joking.

Dr S.I contemplate its pointless and confusing to train children something enjoy this. Stick to rigorous maths please, not some gimmick. I contemplate you'd need to study mathematical analysis (and know more about number systems) before being able to select whether his 'proof' is honest anyhow. Maths is an incredible subject, I would not want my teacher to fabricate stuff up each day...

Mr SpockThe relevance of Dr. Anderson's discovery is "nullity".

retiariusWhen I was a boy (Here's one from the "young-whippershapper department"), they programmed aircraft simulation systems for NASA (in Fortran and assembly language). These were critical models tied to realistic cockpits that moved and shaked test pilots -- they often tried to divide-by-zero due to programming bugs, poorly-understood equations of motion, etc. So, in "real life", when threatened with div-by-zero infinities, the motion simulator didn't just smash the pilot into the cabin wall but rather gracefully smoothed the first derivative into relative soundless by ignoring sum digital computer output, inn favor of an analog "mechanical limiter" override.

David StevensI will not accept any proof that has been released on a proprietary (realplayer) codex, where is the proof!Real mathematicians accomplish not train kids until the math community has verified there proof, even if this is proved to be honest i contemplate he is being very irresponsible teaching unproven methods that are not in the "curriculum" its just plain irresponsible he should be suspended pending an investigation.

ArjunDr Anderson's Axioms: 1/0 = Inf, -1/0 = -Inf and 0/O = Nullity Using these axioms.. 0 = 0 * 0

Gerard KrupaThis man is out of his mathematical league. He has clearly based this 'proof' not on mathematical rules but on the IEEE 754 gauge used in most microprocessors that defines 1/0=infinity and -1/0=-infinity. In unadulterated mathematical terms infinity is non a number and generally considered to be unsigned. Incidentally, to deomnstrate how accurate IEEE 754 is, it besides defines 0 and -0 as two different numbers. As for computing it does not matter in the least whether you picture the result of a division by zero as infinity, -infinity, NaN (Not a Number, a symbol already used in computer science to picture an undefinable result) or some fresh symbol made up by an academic looking for his 15 minutes of fame, you soundless absorb to handle it as an exception and not carry on trying to drudgery out calculations based on a non-number.

FIN AnonymousThis is clearly just a crack by Dr Anderson (I hope). Actually many people probably arrive up with this thought of 'nullity' at some point of their lives. I recollect thinking about this problem with my friend when they were 11. They came up with the same idea. Later, when reading 'real' math books at the age of 16 they erudite about Riemann sphere and were extremely delighted with the fact that they had arrive up with similar ideas earlier. If someone takes this article seriously, I hope he only considers if it would be a usefull thing to train to children. NOT that it would absorb ANY MATHEMATICAL significance. I personally contemplate that this should not be tought. Instead children should only be encouraged to ruminate the problem of dividing by zero (and besides other 'problems').

QuicoHey BBC, the Innocents Day is the 28th, not the 6th. You missed by 22 days. Does any of your computers already implent this theory on its calendar's mathematical engine? withhold in humor this fresh is in the "People" section, not in "Science" section, so whats relevant here is the Dr doing "something", not the "something" he does. Welcome to the Yellow pages. Ok, no more joking. The Dr uses terms ment to present the circumscribe where some sequences lead as if they were conventional numbers suitable to be used in conventional arithemtics, and this is a HUGE error. There should be some free sits on any Berkshire's 6th shape College math course for the Dr and the journalists reporting this to seize edge of.

Somebody987This is stupid. Introducing a fresh number that would picture something is not a solution. And on the other side: Computers CAN DIVIDE BY ZERO (IEEE gauge for floating numbers) - the result is a special "number" called NaN (not a number)! So this problem with introducing a fresh value has already been "solved" long before this (but it's not so practical) and therefore don't listen to this hoax.

Ludovic ClaudeActually there is nothing fresh here. In many computer languages, you absorb a symbol that's called NaN (Not a number) and this is the result of some impossible mathematical operation such as 0/0. The program doesn't crash when you convoke 0/0, it simply return NaN (or let's convoke it -0- enjoy this guy did), and then it can report that there was an error to the user. So this 'number' is only something is only that's convenient to employ with computers, but it's certainly not a sound theorem and has no meaning in number theory (the offshoot of maths that tries to explain and formalise numbers).

sulanJust another picayune "discovery". Anybody can invent a symbol and convoke it a solution of a problem....

joeFrom a computer science perspective any programming language used to create software can detect and entrap 'divide by zero' errors. This fresh nullity symbol has no edge to software. From my limited understanding of mathematics, I would contemplate that nullity is similar to the 'i' symbol used as the result of the square root of -1.

AndyA lot of spurious proofs for x=y where x and y are 2 different numbers reckon on division by 0. Does Dr. Anderson realize that adding nullity makes makes his mathematical system meaningless? Is this nonsense being taught at the University of Reading? The Dr. should hang his head in shame.

ThoronAny computer program what runs whatever piece of equipment (planes autopilot, car, etc.) and divides by zero is poorly designed and the programmer should be fired from drudgery ASAP :P There are error handling techniques and workarounds of the dividing by 0 problems, if you can't accomplish that in your computer program, don't program at all.

NLI know how to avert computers from crashing at division by zero: don't accomplish such silly things.

The JokerThink the title should absorb been different. Total collapse in British traffic - Professor at Reading invents the Square Wheel.

sWozzi3You absorb to watch teachers, my maths teacher tought us that there is a maximum number, I don't recollect what it was but apparently if you add one to it then the result is no longer a number

george Woodrow IIIThis is just nuts. First off, this was not a problem for Pythagoras because ancient Greek math had no zero. It was not a problem for Newton because of his employ of fluxions and infinitesimals and not the modern notion of limits. 1/0 is not infinity. The *limit* of 1/x as x approaches zero from above is +infinity. 0/0 is undefined mostly because in different contexts, it can be 1, 0, infinity or just about any other number. In computer science, there is a symbol for nullity already. It is NaN == not a number. Any well written computer program will not only deal with cases of divisioj by zero, but a host of other problems. I suggest that Dr. Anderson review Calculus, analysis, number theory and basic computer programming before suggesting that a problem has been 'solved'.

UK Anon.A few minor points ... 1. Dividing by zero is not an "unsolved problem", it's simply undefined. It's not a question that needs answering, it's a non question. There are lots of sections of mathematics where functions seize undefined values. It's not a problem; it's fraction of how mathematics works. 2. There is no simple pass of removing these troubling points in the genereal case. examine up sum of the drudgery on offshoot cuts that has been done in the field of computer algebra. 3. This is hardly new, examine up true projective geometry; it's over a hundred years old. 4. Whether or not division by zero is defined, and what it is defined to be has *nothing* to accomplish with problems with computers dividing by zero. examine up NaN in the IEEE floating point gauge or the divide by zero signal handler in POSIX. This has already been solved as much as it can be; it's just most programs are badly written and don't fabricate sensible employ of these features. I esteem that not everyone has a masters degree in the relevant district of mathematics but is there any casual you could check this sort of thing in future?

GrahamIf 1 divided by 0 = infinity then infinity times 0 = 1, no? I sigh the safe Doctor has establish that making a contrast in the true world is a bit hard, so he comes up with this fresh discovery in the virtual world instead.

Alf P. SteinbachTHERE ARE NO DETAILS AVAILABLE ON THIS PAGE. gratify reconsider your employ of obscure video formats. That said, 0/0 is indeterminate and so not a useful concept. x/0 where x is non-zero is sometimes useful (examples I recall from 20 years ago included Lagrangian interpolation and Dempster-Shafer evidence combination). But while multiplying and dividing such entities works nicely, addition and subtraction sends you off into an infinity of fresh kinds of entitites, not very useful. So I assemble Anderson's scheme must be guided, but it would positive be nice to know exactly what it is, which isn't workable when it's presented in that video format instead of simple text.

AnonThats numberwang!!

LordstarWHICH CRAFT!!!!!

JoeNow this is just ridiculous and helps no-one. Publishing such nonsense (as shown by numerous posters below) just contributes to the public's ignorance. poverty-stricken show.

BradfordThat's not whomever he claims to be. That's Al, he cleans my pool on Wednesdays.

MichaelThe result of 0/0 isn't any "normal" number. So he just made up a fresh one. That's quite similar to calling the square root of -1 "i". Imaginary numbers are a useful concept because you can actually fabricate fresh calculations with them that even gyrate out to be applicable to some real-world phenomena. Can you actually *do* anything with this "nullity"? If not, then this is indeed useless rubbish. And it better be more than just motto "combining nullity with anything gives nullity" because that concept has been around for a while and is called "NaN", Not A Number.

DavrosWhat the heck are you sum talking about? I'm Skaro's greatest scientific mind, I created the Daleks and conquered half the known universe, but I've got absolutely no thought what this is sum about, even though I've had it explained "simply" to me. Teaching this to children might be very easy, but can anyone explain this comprehensibly to an adult?

Justin SmithThe problem is that a/0 is the number such that (a/0)x0=a but ANY number x0 is 0. In Nonstandard Analysis (developed in the 1960's) there are infinitesimal numbers (infinitely little but NOT 0) that can be used to define calculus without passing to limits. Perhaps this is related to that?

JonyDr Anderson seems to lack an understanding of maths. He's making the common mistake of treating infinity as though it were a number. There's nothing fresh in his "proof" at all. true academics test their drudgery by submitting it to journals where it is criticised and reviewed by their peers - experts in the field. Not by testing it on year 10 children and BBC reporters! This guy is a crank and shouldn't be passing on his misconceptions to schoolchildren. Or BBC readers for that matter. Don't believe a word of it.

AuctoriThis is not particularly helpful (or even new, at least for computing). The IEE754 gauge for binary floating point arithmetic (used to discharge floating point arithmetic in computers) already defines values to deal with this situation. It has a special values called NaN (for Not a Number) which allow computer programs to resolve problems enjoy divide by zero gracefully.

Some norwegian mute guyI contemplate this theory is ridiculous. The entire "proof" is ad hoc, you could easily write out 0^0 to the fresh expression (0/0). The professor then "invents" a number called nullity which is not on the habitual number line. That is, he designates (0/0) to a value "nullity". Well guess what, it is not on the number line!

RachelTo those motto this is some kindhearted of 'hoax': This is not a hoax. I was taught by Dr Anderson at Reading Uni while studying Computer Science. He used to relate us about his drudgery to unravel this problem.

AnonymousFor sum of you that contemplate that root of -1 has not got a symbol... well... it HAS, the nimber is calles 'i' and it's a complex Number. Fukkin a+ib, where a is a true part, and B an Imaginary part. It's basic algebra, fools.

AlexMy doubt is that by creating a fresh number sistem {Z + nullity} or {R + nullity} you should redefine the basic arithmetic operations and verify (for example) that they constitute Abelian groups just enjoy their gauge behaviour in Z or R.

FireStormOk, I am a programmer and far from being a mathematician, but here is how I absorb always pictured something divided by zero. First, let's accomplish division by a true number. I absorb six apples, if I divide those apples into 2 baskets, I am left with 3 apples, or to be precise, 2 baskets with 3 apples in each. Basically, I created 2 groups of 3. Now, using the same six apples again, what if I divide those apples into 1 basket? I am left with 1 basket of six apples. I created 1 group of 6. Ok, simple. What if I divide the apples into 0 baskets? Well, I would not be creating any groups at all, so I would absorb no groups with no apples. I accomplish not absorb a basket to reclaim the apples in, so I am left with 0 baskets of apples. To me, divide by 0 and you Get 0. same as multiplying by 0. If you are creating 0 groups, there can't be anything in the groups since there are no groups to reclaim anything into. Seems simple enough to me. I contemplate the problem lies in the underlying logic that calculators and computers use. As a programmer, I always check to be positive the I am not dividing by 0 before actually doing the division. A lesson erudite the difficult way. So if I absorb x divided by y (x/y) I first accomplish a simple if statement on y (if y > 0 then x/y) to withhold from encountering errors. Just had to add my null cents. :)

Tom KnightA computer scientist came up with this, not a mathematician? Sounds a shrimp hokey to me...

Tompersonally, i contemplate there is absolutely nothing in such fresh fangled gimickry

K.Ok, having just seen the video clip of his "proof"... I would sigh that he's just re-defined the statement "x/0 = infinity" to "x/0"="nullity", where x is a true number. He might as well sigh "x/0=smiley face" and it'll stand for the same thing!

G. DuttGenius. Will now explain why my bank account is always 0 when the wife's been at it.

Bonjo NelsonBut what happens when you divide zero by nullity? They need to know!

PThis is just symbol. What's the news? How much is nullity+5?

Nathan SkeneBefore sum you people retreat blathering on with your tirades and rants, you may want to desist and respect that this guy is a professor in a safe department. He has actually thought about these issues, there are many applications of these, and he isnt doing it for no reason. You may wish to retreat examine into the Perspex Machine, Perspex neurons etc, the list continues onwards. Or you may be enjoying your ignorance.

IsrafelInventing fresh numbers, that's just cheating.

PythagorasIf I absorb one apple and I give it to no-one, how many apples accomplish I now have?

John PearceyComplete rubbish. Zero divided by zero has answers depending on the situation governed by the functions proximate to zero used in each particular case. These absorb been solved by Newton and indeed he developed the theory of calculus to unravel such problems.

Matthew Sealey, Genesi USA, Inc.Computers divide by zero sum the time; they don't crash if you can entrap the CPU exception it causes. And if you entrap the exception, the value you Get back is already a mathematical gauge - NaN for "Not a Number". As far as I can contemplate this performs the same employ but makes Not a Number a true number, but a practically useless one. As a computer science 'professor' he should already know this, and contemplate that there is absolutely no capitalize to defining a all fresh 'not a number'.

anonymousI withhold popping in and out of the future. There's nothing icy about this. You've killed us all.

Chuck NorrisI could absorb told you sum this years ago.

SteveI am absolutely furious that a respectable broadcaster suchas the BBC would lower itself to publicising this nonsense. There are any number of flaws I could point out in this guy's 'work', but I shall desist at just the one: His 'proof' that 0^0 = -0-. In the final few line he uses the reasoning (0/1)*(1/0)= 0/0 = -0-. However, You can just as easily sigh (in his twisted world of artihmetical fallacy) (0/1)*(1/0) = 1/1. And furthermore, if this concept is so rigorous, simple, and useful, why can't they absorb video of him teaching it to people who actually absorb a smooth of mathematical understanding? Mathematical professors? Hell, even university students? Oh right. Then they would laugh in his face, and that would hardly fabricate for a sensational science legend for the BBC now, would it?

ChrisI absorb a theory as well - Majority of people are bit stupid, pardon. So by analyzing the comments, I find 80% negative and 20% positive(do the math). He did tie number line together! Publicity he got is bad, why? He gets both criticism as well as demonstrates this solution to majority for any casual of adaptation if things are right...Some comments especially examine enjoy from medieval times, where if one would sigh to you- EARTH IS A SPHERE! would Get response - THAT IS PREPOSTEROUS, ITS FLAT!... contemplate about it

AnonymousI DIVIDED BY ZERO OH SHI-

winrarthat FOOL he will raze us sum ;_;

FredrikSeriously, computers absorb been able to deal with floating point divide by zero for a very long time, resulting in inf, -inf, or NaN (not a number) respectively, which are sum sound floating point values according to IEEE 754. Calling NaN nullity is just putting a fresh label on it.

MScThis drudgery is artifical. Why? The Dr is mixing between symbolic definitions and true(real world) computations, i.e 1/0 (def)= inf; doenst picture the true world infinity which is uncountable.

Andreas MarschnerIn the field axioms you can read: To every element x from F without {0} there is a inverse called ((x)^(-1)) (or convoke it enjoy you want) so that x * ((x)^(-1)) = 1 where 1 is the identity elemet of the multiply group and 0 of the additive group. So one can sigh that 0 does not belong to this set of invertable elements. Its every time the same traditional trick to change the axioms by adding some wonderful fresh elements (here called nullity or something) and 'Hooray' here it ist the solution of a thousands of years traditional problem. Dr. Anderson, this isn't very helpful!

Mal LansellComputers absorb been doing this for years - it's called NaN (not a number). Dr Anderson supposedly teaches computer science - he should be fired.

phaunaBut what is x/nullity?

Dr. ObviousSo they sum know that 1/3 is an irrational number, right? Perhaps not! Define 1/3 = Lambda Now I can divide 1 by 3 and Get a rational result, it's just Lambda! Oh those silly mathematicians.

Class DunceThat's total rubbish. He didn't prove anything at all. The concept of numbers lying off the number line is already established (e.g., sqrt(-1), or i), but his number doesn't even absorb that rigor or functionality. I.e., nullity does not equivocate in the complex plane, but in his fresh plane containing only one number. That's the all reason why *most* computer systems cannot deal with it. But in Maple or Mathematica it's handled quite easily as an exception. Furthermore, his "proof" circles back on itself and he uses to definition of his capricious number to "prove" the number.

Will PerkinsPacemakers don't desist when they divide by zero. Divisions by zero are handled in computers by the programmers, no need to worry. This guy is practically using a shape of terrorism, scaring people into believing the weight of his 'invention', to Get it noticed.

DouglasSuppose x-y=0 Then 2(x-y) = 0 So x-y=2(x-y) Divide both sides by x-y: 1=2! THATS WHY YOU CAN'T DIVIDE BY ZERO

Dominic ConnorThis is silly and trivial. He's defined a thing with the properties that it does what he wants. It's actually inaccurate to sigh computers can't cope with this, since they've had a specific "value" for this sort of junk for decades. I'm not positive why you refer to Reading as a "university". This is a status the BBC reports as closing down it's physics department because it's too hard. Lecturers at Reading should stick to folk dancing and knitting, leaving academic subjects to grown ups.

ed dekkerIt seems enjoy sum calculations soundless desist on reaching 'nullity' so the autopilot soundless crashes the airplane. BTW There already is NaN (not a number) in the IEEE spec.

JasterBut the problem is not dividing by zero it's doing anything useful with the reply 2/0 = Nullity 3/0 = Nullity ect... So Nullity*0 = every workable number This was always the "problem" and it soundless it ...

George OuAre you BBC idiots qualified to review this? absorb any of you taken Calculus or even pre-Calculus? 0/0 and 0^0 are both defined as "indeterminates". That means having no numerical value or meaning. This is defined in the dictionary, examine IT UP! This was the genius of Newton where he looked at the rates at which those numbers approached zero and came up with calculus to figure out what 0/0 and 0^0 actually mean. Not just some arbitrarily defined number "nullity".

keshi contemplate he's just reclaim a fresh designation to error detection

AMERICAWhy don't they just convoke it negative zero or something. It will stand for exactly as much as whatever other capricious designation they choose: exactly nullity.

AlphaAXPThis theory looks itself a lot enjoy the own result it referes to: a nulity. "A" quantity, even if abstract, can be defined, not "Any" quantity. amusement but not original. math already owns a symbol for "Any value": it's a capital "A"O upside down.

Roger McJoeSo, in other words, "nullity" is just a fresh word for 'undefined'?

Poeawwww......there goes the fun of attempting to divide by zero :(

Christopher MorrisMathematicians absorb announced the actuality of a fresh all number, which lies between 27 and 28. "We don't know why it's there or what is does," said Cambridge mathematician Dr. Hilliard Halliard. "We only know that it doesn't behave properly when reclaim into equations and that it is divisible by 6; though only once."

Mattwhat a crock of NaN

Markus F.This fresh definition solves nothing. In fact, it just hinders. The professor points out that if an autopilot divides by zero, the plane crashes. Now, if an autopilot divides by zero, and gets nullity, then what? You cannot multiply the throttle by nullity. Worse, still, it forces the computer to spend processing cycles carrying on working with an obviously wrong answer, rather than just revise itself the traditional fashioned way. This just gives a designation to a problem rather than fixing the problem. An analogy would be forgetting to dress in the morning, heading off in your pyjamas, noticing on your front porch that it's rather chilly, but instead of heading back to Get dressed you define yourself to be in a situation of pyjamaity and withhold going to drudgery anyway.

GDWhen people need a number that doesn't exist they fabricate them up. Negatives, then imaginarys, then infinities (Cantor's aleph-null etc) and then now this.

AnonymousI won't employ true Player (same on you BBC) but from the white board in the image it's limpid the safe Doctor is making a huge mistake. He starts with 1/0=Infinity and -1/0=-Infinity. If this is honest then, from very basic maths, Infinity*0=1 which is obviously rubbish, and his all theory falls down from there. If he taught this at my child's school I'd be very unhappy.

A mathematicianReaders who want to know more can find the author's papers on the topic via Google. Personally, I don't rate them, and I contemplate teaching an unaccepted (some sigh crackpot) theory to school kids is a really despicable idea; if they start parroting this nullity industry in their exams, they'll lose marks.

DomThat's a completely circular arguament. You can't unravel the problem of dividing by zero by inventing a number that *is* something divided by zero and using that. That's enjoy motto "How many children are there in the mediocre family", and solving it by motto that the number of children in the mediocre family, minus one, is x, so the reply is x+1. There. Solved for sum time, aren't I clever.

Johann PetrakThis guy obviously does not understand math and I am troubled by the thought that he teaches kids. Any second semester math student should be able to relate him why his shrimp trick is not only utterly useless, but besides leading to more wretchedness than it is solving. If this is not a hoax: please, BBC reporters, accomplish not spread nonsense just because it comes from somebody with a "Dr" degree. Next time you will relate us about somebody who has constructed a perpetuum mobole or squared the circle, right?

Lawrence DimeryI contemplate Prof. Hubert J. Farnsworth has a sound point, not so positive about the wealth of professional mathematicians getting in their own two penn'orth. The only one to fabricate a decent point is Peter H who fights and beats Dr Anderson on his own paper-thin ground.

Ben GoodgerNullity is equal to x/0 as much as sqrt(4) is equal to 4i. This isn't a solution to an impossible problem, it's a workaround. When you absorb a decimal value of nullity, I'll employ it...

JoeDr Anderson wasn't the first to invent a symbol for a devide by 0. Computer programmers 'solved' this problem ages ago. On a computer, dividing by 0 doesn't antecedent aeroplanes to crash - it just gives the result as NaN(not a number).

HerbertAnother designation for 'nullity' would be NaN for those speaking javascript for example.

Chuck NorrisOnly Chuck Norris can divide by zero!

Frenchy McBritishThis is ridiculous. I've been using nullity for years. Only instead of "nullity" I convoke it "socks." And by "using" I stand for "wearing on my feet."

KristofUIt's just the NaN made formally in algebra. Computers can already accomplish this, and not crash at all.

ChristianInventing a fresh nubmer doesn't unravel anything? It's almost enjoy NASA should say, "Well, they can't travel to Jupiter, so they renamed Mars to Jupiter. Now they can travel to Jupiter."

Karl BuysI contemplate he should be hailed as Professor Maths Adjectives, because he's not doing anything else besides describing the concept of how division by zero is undefined in the sense of quantitative values. They solved this problem long ago by defining division by zero as being "Not a number.". Chris Croughton summed it up earlier. If you request me, this guy should rather try to arrive up with a useful theory, instead of redefining a concept such that it makes him examine smart. Pythagoras would say, "You, me, in the parking lot, now." if he was soundless alive. Arguing semantics has no status in mathematics. Neither does a marketing team. Invent a useful theory if you want to be hailed as a professor of mathematics.

g33kThis is nothing new.. Chuck Norris could already divide by zero by roundhouse kicking his calculator first

thoughtsold news, the thought of dividing by zero has been covered several times in mathematics, but with points ouside the number line, and besides points at infinity, infinitessimals, transfinites and so forth, this is a step backwards, if anything, and certainly nothing new

SwedeThis guy should absorb his brain examined. The country Sweden is laughing and asking them selfs - Are sum englishmen this stupid? I contemplate you need to change your diet!

Mr GentlyI tried this on my calculator, it just said "A suffusion of yellow". Again.

lame"which solves maths problems neither Newton nor Pythagoras could conquer" yup sounds enjoy a turkey, didn't need to read the article after this

John RyanWe absorb life for 1200 years not needing to divide by zero, so why accomplish they need to know?

MarkusI define sum of the world's problems as monkeys, therefore they don't absorb any more problems, just monkeys. Let's retreat contemplate if it made a difference!

JasonIt's just a fresh label for the same result. Wether the computer says "error" or "nullity" the plane will soundless crash. "Raise the flaps by nullity%" - it won't aid you land. If your pacemaker decides you need "nullity" heatbeats per minute I contemplate you'll soundless dead.

MatteoOnly Chuk Norris can divide by zero

Claus TonderingRubbish! Using his technique I can prove that infinity is zero: (I employ ^ to indicate exponentiation and * to indicate multiplication. I besides employ the fact that 0^2=0 and 1^2=1) infinity = 1/0 = 0^(-1) = 0^(1-2) = 0^1 * 0^(-2) = 0/1 * 1^2/0^2 = 0^2/1^2 * 1/0 = 0^2 * 0^(-1) = 0^(2-1) = 0^1 = 0 Hence infinity=0. Rubbish.

Year 13 Stats ClassWhat a load of....We contemplate he is giving mathematicians a despicable name. They are not sum miserable people that absorb nothing better to accomplish with cur time than fabricate up fresh numbers that aren't even true!

ErinyesThis seems to be just another representation for 0/0 but not any solution to me. That pass anybody can define a symbol to any unsolved equation and sigh he/she solved it.

KasyxYeah, they can't divide by zero so they will fabricate up a number that will allow us to...

Class 10M2We understand it but it is totally pointless.Nobody was bothered before so why are they bothered about it now.

Jick RamesMaking up a stupid word to solves that? In that case it was done long ago and the word is "OH SHI-".

BurnRyan: on that circle of yours, isn't the distance between 1 and 0 and between 0 and -1 illimitable as well? Being 0 the only quantifiable number in between... that makes it a focal point in the curve, which has not an inverse beside itself. Or if they coerce it to absorb it, it would absorb two, one below, one above. But as they step away from 0 in any of the two directions they step into illimitable fractions of 1 or -1. How can you situation therefore that 1/0 exists as inverse of 0/1 on the upright line? It would be more courteous to assume that 1*0 = 1/0 = 0.

2 centsWhat does it solve? convoke it nullity or whatever you feel like, it's only a concept, no solution. In software they deal with difficult numbers. A CPU is basically a number cruncher. Nothing more, nothing less. It can't handle a concept. In programming dividing by zero soundless requires some extra drudgery to handle it elegantly.

Wild_UmpireIn the same pass that i (square root of -1) cannot be calculated, and that infinity cannot be calculated, nullity cannot be calculated. sum they absorb defined here is that something divided by 0 is something that they cannot calculate - a problem that soundless hasn't been solved for 1200 years and probably won't be for another 1200 years

CheburazhkaI don't contemplate anything fresh here. Programming languages enjoy C++ employ NaN which means Not a Number to picture division by zero. But it's safer to avoid this division rather than examine for NaN...

Babel fishThen the reply to the ultimate question of life, the universe and everything is in fact... nullity?

MorganI recollect some time ago, developing a 3D realtime engine, putting the camera looking exactly to the 0,0,0 position ended with a divide-by-0 error, I felt that something failed there, there's must be a better matematical solution that permanently adding a fraction to the target of the camera to avoid this error

SagaraSomebody was stupid enough to release this breaking advice in true video format! The true format is not an open format that everybody can use. I read this web page its because its in HTML, which is an open format. When releasing something targeting the world, gratify understand the weight of releasing it in an open format so that everybody can see, read, hear it. If it is audio, Ogg Vorbis is recommended, you may respect FLAC if you are releasing something requires very lofty audio quality. If it is video, Theora is recommended.

Dr. JonesIt's a true pity that BBC runs this kindhearted of advice without confirming them with somebody who knows *something* about mathematics. This is just miserable and silly.

Shams from NorwayThe theory og nullity is nonsense! Everybody know that everything around us whether it is technically equipment, arcitectures and so on are based only mathematic. So why doesnt the socities, communities, and country Fall apart if their traditional mathematic isnt complete, as Dr Andersen trying to relate us. I dont beleive that his theory of nullity give us significant multiply og mathmatic knowlegde og give more helpful in gaining the mathematical solution. Shams B

Mike ScottThe true numbers are, mathematically speaking, a field, which means that they absorb a lot of useful properties that materialize to be intuitively obvious (although of course they're not, you're just used to them). If this "nullity" element is added to the true numbers, they are no longer a field (It breaks either the multiplicative inverse property or the multiplicative associativity property, depending on whether or not you define a multiplicative inverse for nullity), and so a lot of useful results become inapplicable.

Nick SharplesNo, sorry. His definitions are inconsistent: His Definitions: inf=1/0, -0-=0/0 besides he claims that -0- is "off the true line" so -0- is not a true number. From his calculation: -0-=(0/1)*(1/0) But: (0/1)*(1/0)=(0/1)*inf = 0*inf (by his definition of inf) and inf=1/0 implies 0*inf=1 Therefore -0-=(0/1)*(1/0)=1 Therefore -0- is a true number, which is a contradiction. This refutation doesn't employ any abstract notion of infinity, or uses any of the highly analytical mathematics required for dealing with problems of Dr. Anderson's type. Instead it only examines the mathematical consequences of the definitions that Dr Anderson provides. When introducing definitions in maths, only two things are required: The objects aren't defined ambiguously, and the definitions are consistent. Without consistency, they can 'prove' anything in mathematics.

WizkidIt sum boils down to the sum people, understand that when you absorb nothing, something is better than anything. So this nullity gives you 0}0.0 = [´0.1 wich is indeed a fresh number, just retreat with it.

KodHedZin hex, there is no zero, it is a set of 16, and the grouping is defined by the digits (16). in decimal, the zero is used as a placeholder for the grouping mechanism. In reality, zero does not exist. they employ zero as a placeholder in their math, of the 10, which is a group of x * 1. or 20, which is x * 2. but the 10 is now a number itself, which creates a number of the placeholder, but soundless this number does not exist. I feel this is a rudimentary problem. why create something out of nothing, to unravel a problem they created in the first place?

Bob BobbersonHow about it being as simple as this. 0 = nothing, correct? So motto 1 divided by nothing is as simple as motto 1. 1 times nothing is 1 nothing, which equals nothing. Why does this absorb to be difficult?

NinjaTariqSo as you divide by smaller and smaller numbers you minister to infinity, but when you achieve zero it becomes nullity? Its stupid. What happens when you divide by nullity? This solves nothing, this man is an idiot. So they will just rename a divide by zero exception to a nullity exception? You can't accomplish anything with the value nullity.

JoeNewton did unravel this problem with calculus. dx/dy give the gradient of a curve at a point, which is done by making dx and dy equal to zero. Unlike Dr. Anderson's work, Newton's is actually useful for something.

LainI suppose Dr James Anderson is a medicine doctor, because noone slightly confidential with mathematics can arrive with a theory as lame as that. It's just the same as claiming that giving designation to a positive disease cures the disease.

MikeI contemplate if an airplane's airspeed or altitude wanders off the true number-line, it's in pretty solemn wretchedness regardless of whether it calls the result nullity or not. And programs don't crash when they divide by zero unless they're *really* badly-written; for a CS professor to suggest that they accomplish is bizarre.

AnonI tried it, I DIVIDED BY ZERO O SHI-

BobI thought it was only chuch norris who could divide by zero

AdrianHmm. Any number divided by 0 is nullity? Interesting. So 1/0 = -0-. 2/0 = -0-. This gives us 1/0 = 2/0. Multiply both sides by 0, and 1 = 2. Why is it that Reading University attracts sum the crackpots?

Chuck NorrisI can divide by zero.

Dave Taylor0/0 = (1+[-1])/0 = 1/0 + [-1]/0 = 2/(2x0) + [-1]/0 = 2/0 + [-1]/0 = (1+1)/0 + [-1]/0 = 1/0 +1/0 + [-1]/0 = 1/0. So nullity = infinity = [-infinity] (by a similar argument). Moral: Doing basic algebra that involves division by zero generally produces nonsense. Mathematicians already absorb ways of handling infinity and division by zero, which are treated very carefully to avoid stuff enjoy this.

MathematicianWell, I contemplate that the point that the Doctor is trying to fabricate is that 0/0 = , and sum he wants to accomplish with nullity is to fabricate positive that you Get one thing which means "any number". This will probably fabricate life easier for computers. I'm not so positive that it makes life easier for the children at Highdown.

fozzmeisteryou cant divide a number by a number and Get an absence of number-and-type (which is what null is). It's undefined. And no this will not unravel programming problems, it just moves the problem on a notch to the next level. plain Stupid, -1 points.

Pete Morgan BScHOAX. So what is Zero to be then. Apollo would now be permanentely on the launch pad if 5, 4 ,3, 2, 1, nullity .. so they sit here forever. And as a programmer myself, they already got a workaround for div/0 errors. Almost 99.99999% of applications do. This is pitiful and am surprised the BBC has been mug enough to fabricate a feature of it. gratify remove this nonsense ASAP.

MEEO_o oooOoo.. enjoy i care??

Computer ProfessionalHas this actually been published in a peer-reviewed journal or has this only been topic to review by Year 10 children and gullible reporters? Are there any meaningful results when operations are performed on this fresh number? Does associativity hold on those operations where it would hold with other numbers? If not, then it isn't a number. Offhand I would sigh it either looks enjoy something useless, or as someone else has already pointed out, no different than the NaN that computers absorb used in floating point math for 30+ years.

KarolineHAHA.. u cant just start a fresh mathematical invention.. since it has not been figured out in enjoy 1200 years, and now suddenly this "dr anderson" invents "nullity"? its weird.. its not eccentric dat nobody has ever figured this out, since they didnt contemplate about "the fanciful no-problem nullity!".. strange!

RikThe solution to x=1/y as y tends to 0, is that x tends to infinity. The solution to x=-1/y as y tends to 0, is that x tends to negative infinity. The solution to 1/0, however is undefined. You can indeed just fabricate up a number and define the solution to be that, but it's not terribly useful. Compare this to the square root of -1, which although equally unfathomable, has been defined as 'i', and actually has some use.

Ævar"Computers simply cannot divide by zero" is wrong. Computers don't implement math (for instance they absorb a limited integer range) and the handling of n/0 depends on the processor. Sometimes it's NaN as another poster mentioned and some processors enjoy the PowerPC allow intiger division by 0 (n/0 = 0)

AnonymousEvery time I divide by zero, I just Get "oh shi-" on my calculator.

Tony (Cambridge)The safe advice is, that whenever they absorb difficult to unravel mathematical problems, it's no longer difficult. Just invent an fresh number.... problem solved... this should foster mathematics infinullitesimally.

Hal JordanFunny how he picks Green Lantern's symbol for nullity.

Salim SiwaniThe concept isn't new. Computer programmers absorb been using the thought for years. To fabricate software robust you absorb to check to contemplate if your about to divide by zero. If you are, then simply return a sensible number in its status (I employ 1.0 most of the time). A divde by zero usually comes from some error condition and returning a sane number back usually gives you a stablising effect that means your software won't blow up.

RobertI enjoy this theory, it just isn't a solution, just another pass to request the question. For me(and I contemplate most others): x/0 approaches infinity, x^0 = 1( by definition), 0/0 = 1, 0/x = 0, x/infinity = infinitely little (very proximate to 0) These drudgery always unless you seize x=0, then is is 0/0 = 0,1 or infinity, but when will you accomplish that?

Haakon Bernt EilertsenDr Anderson has not provided anything that is unknown to a safe student of functions. Since some functions are irregular near some points as the denominator tends to zero, they may introduce a fresh abstruse number (variable)which may answer any equality with "old" numbers. This fresh number solves sum formerly called indefinite expressions and undefined expressions 0/0, 0 to 0-th and so on.

SebWell it's just the same principle as the square root of -1 being the imaginary number i, nothing to contemplate here gratify inch along...

Jim MooresA lesson in how to embarass one's self and the BBC internationally by not checking that your ideas aren't stupid with the Maths department down the hall.

Duncan LorianderThis 'theory' is as much nonsensical rubbish as timecube theory. And at least timecube theory is droll as sum hell.

BenderThere are so many problems when he tries to unravel the problem. The expression (0/1)*(1/0) cant be turned into 0/0 since 1/0 is infinity and they can't employ the ordinary simplification rules that they employ for fractions. It totaly alright to introduce this definition if it makes math better, but since it only is humbug and replete of contradictions, it is of no use. It must be of limited employ in computers also, you can check for division by zero and employ exception handling. There's really no need for this.

Taxpayer NorwayApperantly, the tax offices here in Norway has known how to devide by zero for many years... They reall do!

SlashdoterRead slashdot about Dr. Anderson

Ijonas KisselbachComputers absorb always been able to divide by zero. The result is always "divide by zero error", which is no less useful than "nullity". Its sum in the interpretation.

arild haraldsøit`s easy..thats it!!

Suprised American MathematicianWow, that has got to be the /dumbest/ thought I've ever heard. Thank you, Britain, here at Texas A&M they in the math department would absorb hung this guy before he could fabricate a mockery of his school. I'll recollect to ignore math papers from the "University of Reading."

in3rtiaSeriously, He created a term for something and then said it exists... HAY GUYZ... LET'S FIX THE PROBLEM HERE 0/0 = ɤ OK? why?!?!? well cause... it is!

BryanSo 0/0 has been given a fresh label - nullity - and other fractions with a zero denominator can be expressed in terms of that. I don't contemplate anything fresh or practically useful from this. The theory of complex numbers (which is extremely practically useful) came about in a similary pass though - convoke the square root of -1 'i'. Can anyone contemplate this mechanism yielding similarly useful theories? (I can't myself).

RexMI did a paper on this, as a sophomore (I think, Im went to a swedish school). I introduced some silly symbol representing 0/0, then I used it to unravel tan(0) and some probability equations proving I was a superhero somewhere in the universe... I got a c- :)

Haakon Bernt EilertsenThe solution proposed by Dr James Anderson ought to be well known by anybody with scholarship of true functions and their behaviour near points of discontinuity. As the denominator tends to zero, the function value may minister to infinity or any number depending on the particular function f(x). So simply define a "number" (actually a variable)which may be interpreted as "any number or infinity". Then as is well known, the problem of dividing by zero is solved. The vital issue is the fresh feeble equality between the fresh number and any traditional number.

NaNThis is just a horrible paper based drudgery around that isn't required. There are already enough ways of handling this. Computers absorb divide by zero exceptions , and us meatpiles absorb infinity.

OersoepThis brings us to the question: "Is a workaround a solution?"

ValentinEither this guy is an crack or someone just misunderstood him.

PhilipAny number divided by 0 tends toward infinity.. given that infinity is one really broad number I cant contemplate this solution being much employ in computing without being either wrong or highly inaccurate. (1/1 = 1, 1/.1 = 10, 1/.01 = 100 ... and so on down to 1/0 .. maybe a graph might be a better shape of explanation. you could ever reclaim superman on the discontinuance of the line flying off into the wild blue yonder.)

Ben1/0 why is that always regarded as positive? If they approach 0 from left hand side, then it approaches -infinity.

StanSimple logic :-)

ainyvetigreYou can't divide by ZERO, so in my very humble sentiment no action is made on a number that is being divided by zero, so: 4/0 = 4 (no action taken on 4, since dividing by 0 is impossible) That imho would unravel the problem.

Ed LoachIn his workings Dr Anderson doesn't only define "nullity" as a fresh number - he besides defines 1/0 as infinity and -1/0 as -infinity. The answers to these two calculations are undefined, otherwise you can besides prove 2 = 1 (2 = 2 * 1/0 = 2 * infinity = infinity = 1/0 = 1). Infinity is not a number (and indeed there are an infinity of infinities when you Get into the maths...)

blue_jesterYou can't just add something in to fix the problem that is just bending the rules. If I had of tried this in an exam, complete with a justification, you know it would absorb been marked wrong and you would absorb been burned at the stake for even trying it

JeffThis is similar to the the invention of the number i sqrt(-1) which has sum sorts of practial applications except this assumes negative infinity exists which I accomplish not believe has been proven

PevPatrick Bampton> A 'RAM' file is a true Media file - the same as used sum over the BBC advice website for audio and video.

USAUgh... The British are at it again...

AnonymousExcellent, this is fanciful news! Who wants to link me in pursuing a multi-million dollar research vouchsafe to flip the world of mathematics on its head AGAIN by proving that "nullity" equals zero?

Simon DaySo if this fresh "nulity" line sits perpendicular to the true number line, then where does it sit compared to the imaginary number line? Are they now going to absorb Anderson space as a 3 dimension equivalent of Cauchy-Riemann space?

DavidHaha :-) What a droll story! It's not even the 1st of April!

Per JensenName it what you want, it's soundless dividing by zero. I used to train computer science, and when they discussed zero division I used almost exactly the same "proof" as a joke. droll maybe, but brilliant it's not.

/dev/nullFor anything to be useful, one must be able to accomplish something with it. How can this 'new' number be reclaim to use? e.g. the concept of 'imaginary' numbers ie. sqrt (-1) can be useful in advanced calculus. So extending the thought of use, what can nullity be used for? Is it, as people absorb said, just something that someone has chosen to name?

BarneyGThat guy is trying to be smarter than he is. His theory is plain stupid. He should try this instead: a^2 - a^2 = 0 -> a(a-a)=(a+a)(a-a) a=a+a a=2a 1=2 (!) or 0=1 Now i proved it :o) you can easily devide by 1 instead of 0. :o)

HoshimtoMr Anderson's soundless animate in the MATRIX world. This is just not possible, assumptions can provide solutions to many unsolved problems which soundless discontinuance up being problems unresolved. enjoy I'm assuming him of not being a doctor.

DanCould he not explain it on the website? Why accomplish I absorb to watch a silly true player video?

davidThere are three main problems here. The biggest one is that "nullity" is homomorphic to "indeterminant", so he hasn't solved anything just gave it a fresh name. Further problems involve 1/0 not being illimitable (this cannot be goten around with either limits or more basically epsilon-delta), and that he has claimed besides that 0 x infinity = nullity, which besides isn't necessarily true.

LindaI conform with Sam

Christian BauComputers can't divide by zero? gratify relate that Professor Kahan. And maybe the guys at the Institutie of Electrical and Electronics Engineers at www.ieee.org need to be told that something is missing in their IEEE 754 gauge for floating point arithmetic that about every computer since the mid 80's is using.

J. TvorupThrough history, many geniouses absorb been laughed at for their theories simply because it couldn't be right. Some years later, they were proven to be right. Therefore I normally would give the thought the capitalize of the doubt, but this simply does not fabricate sense! If I absorb a cake, and I would enjoy to divide it between zero people, how large a piece would each person get? It does not fabricate sense. I admit, I accomplish not fabricate aviation software, but I accomplish believe that it is the gauge procedure to entrap the divide by zero exception , absorb the software ignore that calculation (or whatever your strategy is), and recalculate. Maybe give an alarm to the crew so they can seize over manually. In any case, it would be much easier to handle an exception than some number they don't know between negative infinity and infinity!

Norsman saysthe only fresh to this - is that you gave a designation to what is impossible - and you reclaim the impossible correctly away from the numberline - where it belongs .. rubbish

dbummeno matter what you say, 0*0 soundless equals 0. nullity, as defined by 0 is still, nothing. and if you divide, multiply, add, etc, 0 with 0, you soundless absorb naught but 0. nullity as defined by O, as a variable could excite some entertaining answers. (note the 0 vs O, (or 'o' if you don't employ caps)

gregory haineshehe, so...x/x^2 is continuous now? on the (stealing a name, thanks 'Anonymous') infinullity number plane?

WOWwow... didn't know pacemakers are designed to murder you by dividing by zero. Also, if you weren't aware, 1=2. It can be proven by dividing by zero.

backqwertyThis sounds open the door to more understand how they can apply the theory of the "science fiction" methodes. Any result much better enjoy an error in any case, because you can accomplish something with a result, but you cannot accomplish anything with an error. safe luck.

RAJASHEKARGOUDA.H..Si dont contemplate it replaces the problem, as well the infinity itself is better.

ChrisOk, so by "creating" an imaginary number, he solved this problem? Hell, I could absorb done that! How will this aid computers? What exactly does nullity stand for anyway? If you are dividing by zero, then find another pass to accomplish it, you probably screwed up!

ErikPlease bring advice enjoy this on the date assigned for it: April 1st

w00t!I hear they besides jsut made a fresh colour !

DKObserve that Dr. Anderson carefully made positive no one in the latitude knew anything about mathematics before he began talking...

DaveAlmost sounds enjoy the "i" disclaimer that goes along with an imaginary number, (the square root of a negative number). Now what is the practical application?

I've thought of this beforeAnd it is possible...just enjoy imaginary numbers.

USC StudentI hope this is a crack . . . a very despicable and not droll joke. Nullity? How ridiculous

David JungerJavaScript and some other languages obsoleted divide-by-zero exceptions long ago. sort one of these lines in your browser's address bar and press return to Get the results: javascript:alert(1/0) javascript:alert(-1/0) javascript:alert(Math.pow(0,0))javascript:alert(0/0) For the faineant ones, here is what JavaScript returns in each case: Infinity -Infinity 1 NaN (Not A Number) three of which are special values of the Number type, and much more meaningful than Dr Anderson's "nullity". These values are not errors, they can be used anywhere numbers can be used, for illustration the expression -Infinity+3 is sound and evaluates to -Infinity, and Math.sqrt(Infinity) returns Infinity. Math operations on NaN simply return NaN, they don't complain.

Cynthia GauthierActually, this problem has many implications, which may require or assume a different solution. For instance: [1] You absorb zero pie. Your job is to give an equal slice of pie to zero people. You may not give more than what you have, since you can not create pie; you may not give negative pie either. This case says 0/0 = 0. [2] As you approach x = 0 in the expression 1/x, the result approaches positive infinity. Nothing is defined for the case 1/0, since 0 has no badge per se. This case says the result is either positive infinity, negative infinity, or some kindhearted of "signless infinity". Well... It soundless has no defined value. So there.

ChrisAt one point he came to the formula: 0/1 * 1/0 0/1 = 0 1/0 = infinity (To his theory) so he says: 0 * infinity = nullity But they sum know 0 times something is soundless 0.

Peter NewmanThat's so simple its incredible that it's never been before!

SergeWhy not ? Why reject this ne thought and respect it "heresy" ? THERE IS NO HERESY IN SCIENCE or in maths ! There are concepts that drudgery and some that don't. It took a decision from the Pope to fabricate the occident accept the thought of 0 (zero) ! The number 'i' (where i-sqared is -1) helps unravel mathematical problems. They _work_ ! If this 'nullity' works and helps, it might be good. If not, it will disappear.

GuchieQuestion: Why accomplish they sigh things enjoy 1/0 are undefined? Can't you convoke 1/0 infinity and -1/0 negative infinity? Why not? Answer: 1/0 is said to be undefined because division is defined in terms of multiplication. a/b = x is defined to stand for that b*x = a. There is no x such that 0*x = 1, since 0*x = 0 for sum x. Thus 1/0 does not exist, or is not defined, or is undefined.

Brian C.From what I saw, sum he's done is propound a routine for solving zero raised to the power zero, not dividing by zero in general. What about 5 divided by zero, or 16, or any number on the true line? Now I'm not a mathematician. I'm positive there's more going on here than meets the eye, but it looks enjoy he just grabbed a random greek note and called it zero over zero. More explanation is necessary.

Sean YoungIf the autopilot divides by zero, there is a problem in the programming. Rubbish in, rubbish out. A fresh symbol for rubbish doesn't change anything.

dark.nowhereFor the universal case, 0/0 *should* be an error because of what it is suppositious to represent. I'll rush with the apples analogy: You absorb 10 apples, and distribute them among n people. The formula 10/n represents the amount of apples each person got. Where n = 0, there are no people to even receive the apples, and your apples absorb been allocated outside of the (hypothetical) universe. There are no values left to drudgery with. I'm not a math/physics guru, but I believe there are no practical (read: real) applications for division by zero. When your computer does it, it's because of a poverty-stricken assumption by the programmer, or is specifically being used to raise an exception to the given set of assumptions so that it can be handled as a special case. The only time it arises in math is when operating on computed values , enjoy dividing by a delta -- why would you operate on a delta if nothing has changed? Finally, the person who programmed your pacemaker may absorb opted for a timing crystal sprinkled with capacitors, resistors and diodes. If they were expected to employ a computer for some reason, they're not permitted to be so absentminded as to fabricate the mistake of introducing such a bug. Even so, it's probably besides designed to reset on failure. Hopefully the same goes for the metal birds.

Genius1=1 1/1=0/0 1=0

pdI conform with Wyvern. What he's talking about is called the "limit" in calculus.. they know that [any constant but infinity]/x as x begins to approach 0 will commence to approach infinity (or negative infinity if anything is negative). So, the circumscribe of 2x is 10 as x approaches 5. If it approaches from the left (as in 4.999) it will become very proximate to 10. As it approaches from the birthright (5.0001) it becomes proximate to 10. The problem is, 1/x approaches negative infinity as they arrive from the left and positive infinity from the right. And since they don't know the answer, neither the circumscribe nor the actual reply exist (I think). I'm no mathemetician but making a fresh designation for an traditional problem is not a solution. And motto the reply is between negative and positive infinity doesn't aid us anyways. (what Bob said).

AnonymousThanks for destroying the universe.

teachereither HOAX or poverty-stricken kids, very sad

JoBob, I contemplate you misread something. It says that the conventional number line stretches from negative infinity, through zero, to positive infinity. And not the fresh number, nullity lies in fact outside this conventional number line. (Not that that makes it any clearer for me, might fabricate it clearer for you though.)

Dan1/0 is not infinite, it approaches illimitable but illimitable is not defined. This man is a moron. besides you cant just define a "constant" nullity and title to unravel the problem, hello? NaN already exists as does lots of freaking error trapping values in computers.. Fuck you

ashishthis was the only concept which humans were missing and monkeys already knew. This proves to me that they indeed descended from monkeys ! seize this creationists !!!!

JoshI can't watch the video because I reject to employ malware enjoy RealPlayer, but I feel the need to point out that several responders absorb misunderstood a poorly-worded sentence in the article. The article does not situation that nullity stretches "from negative infinity, through zero, to positive infinity". It asserts that as an explanation of *the number line*. Read the sentence again, and you'll Get it. I too made a double-take on that sentence, but it's not stating anything as hair-brained as some of you are suggesting. I accomplish completely conform with David, though. This won't let us unravel anything they couldn't before. It's simply a notational convenience which allows positive mathematical patterns to be expressed more succinctly.

JesboatPeter H: His theory doesn't work, but your math doesn't present it. The problem is with "But, if 1/0 = infinity, then it stands that infinity * 0 = 1". To Get from the first to the second, you need to multiply by zero, so 1/0 = infinity 1/0 * 0 = infinity * 0 NOT 1 = infinity*0 BUT 1 * nullity = infinity * 0 nullity = infinity * 0 It's well know that defining a/0 to be any true number allows you to present it to be every true number (thus sum reals are equal), which is why dividing by zero is typically undefined. His nullity is not a true number, though. Basically, you seize sum the rule of algebra and fabricate them only drudgery for true numbers, and deal nullity and the infinities specially. Gee, that sounds awfully familiar. Almost just enjoy a limit, in fact. In calculus, the Laws of Limits allow you to manipulate limits (which can involve infinity) using regular algebra as long as they don't involve infinity. There are positive indeterminate forms, enjoy 0/0, which you can't manipulate in that way. Those require special treatment and succumb different results depending on the problem. Leaving aside the matter of defining nullity in a pass which doesn't rupture the rest of math, how useful is it? I absorb to conform with most others here that it's not. It doesn't picture anything in the true world, which takes away any immediate uses. Neither does i (sqrt(-1)), but there's a contrast between them: most algebra soundless works for i. (sqrt(a*b)=sqrt(a)*sqrt(b) is the only rule I'm cognizant of which requires a and b be real.) Almost nothing works with nullity. So, nullity is a fresh "number" which doesn't picture anything true and makes almost sum expressions containing it unmanipulatable. That's why his theory (not a theorem, as the article states) is pointless.

Christer from NorwayIf the solution to a problem is to create a fresh number then he is correct. But how to divide nullity to nullity. stupid man

Tore Sinding BekkedalThe remarks about the computers is patent nonsense. I'll try to explain this without getting too technical: When a computer encounters a division by zero, it is called an "exception". This leads to the processor jumping into some program code it has ready for the purpose of handling this. Now, this code is written by the user. If a gauge program in a gauge environment gets this error, the program which executed the errant instruction will be closed by the operating system (Typically Windows, alas) - this is one of myriad sources for the infamous "Program X has executed an illegal instruction" dialog box in Windows 95/98/ME. However, in a special-purpose and mission-critical applications, which both air planes and pacemakers most certainly are, there are exacting standards specified regarding how this is to be handled. Typically, such an operation would absorb absolutely no effect to the user (the system would immediately recoup from it), and the illustration of the pacemaker is completely absurd. That this comes from a professor leads me to believe either that the article grossly misrepresents his statements, that this is a hoax, or he is clueless.

Simon the AustrianGosh, what a Hoax. One can't just define that infinity equals 1 divided by 0, whats with 2 divided by zero? what pupils should learn in school is that never ever infinity equals another infinity. Depending on your definition of infinity (there can be illimitable amount of different infities created by something divided by zero) you would Get a different result for nullity for each definition.

UW StudentHow is that useful though. i (or j if you are in EE) is useful for describing sinusoidal circuit behavior, also, using i*i you are able to arrive on the true number line again, making previously undefined problems solvable.

AgeethJust a fresh designation for an traditional thing. This this does not help. Probably the exhort to designation something in order to be able to -pretend- to understand it.

PatrikIf you contemplate of it in analytic terms, sigh 5 is divided among sigh 5, then they sum know that each gets 1. Now if they accomplish the same with 5 divided among 0, that must stand for that they either contemplate of it as each gets nothing since no one is to title "their share" or 5 since it has not been divided into any fresh pieces. So, as i contemplate it they absorb to figure out a convension motto which is to hold. Nullity is unadulterated bullshit (please excuse my french). But then again, my own theory will not hold for long, just enjoy Dr James Anderson's theory. Another workable value of X/0, for any X is i. But i as they sum know is not a sound number.

RaymondAs someone else in this comment board said, the fact that somebody proposed the special number doesn't fabricate it "real". In fact, it's demonstrably not true because it sits someplace off the true line, in a plane that could be called the "nullity plane", relatively akin to the "complex plane" that's composed of the true numbers smooshed together with the value i. Then, of course, you can smoosh nullity, i and the true line sum together and Get something in 3-space that appears very, very eccentric indeed. It's probably the status where you can hear one hand clapping, and there are lots of trees falling with no one around to hear them.

Lukosrageif I woke up one day and just made up some nutjob theory, could I be in your advice too?

Scott LambEvery calculus student knows the reply to such questions as "what is the circumscribe of 1/x as x approaches 0 from the right" (positive infinity) and "what is the circumscribe of 1/x as x approaches 0 from the left" (negative infinity). And more usefully, such questions as "what is the circumscribe of (f(x+h)-f(x))/h as h approaches 0 from the right" is the definition of derivative. Integrals are defined through limits as well. This is the very foundation of calculus. But "1/0" alone? What does that even mean? There's no answer. It's a stupid question. The first thing he wrote - "infinity = 1/0" - was already wrong. If he made his arguments to his peers instead of schoolchildren, they'd shoot him down, and rightfully so. Furthermore, motto that computers cannot divide by zero shows a ridiculous lack of common sense. They can accomplish anything they design them to do. Many computer number systems absorb a special value "NaN" (not a number) that is similar to his nullity concept, except that it's not arrogantly proclaimed as revolutionary or a solution to every problem. Generally, asking a question such as "1/0" indicates a solemn logic error. Imagine that airplane needs to calculate the proper elevator trim. Oh, great, the reply is nullity. What does that mean? How should it inch the elevators? Giving this failure condition a fresh designation doesn't change the fact that the airplane's soundless going to drop out of the sky.

mike in sj, calif.next week, the professor will explain perpetual motion.

PhilI'm a physicist (not a mathematician). At first glance I feel cautious but at the same time it doesn't appear any worse than the concept of the square root of negative numbers (multiples of i). I'm positive Riemann would absorb something to sigh about this. Anderson could absorb been a bit less arrogant about it: he's setting himself up for deride if it is shown to be nonsense.

mathmoThis is ridiculous. I can't believe this guy is a professor. Any moron can define division by zero. Here, let R be the set of true numbers. Let / be a binary operation on R that satisfies: (i) 0/0 = 17; (ii) 0/a = 0, for sum nonzero a in R; (iii) a/b = a * b^(-1), for sum nonzero a,b in R, where * is the habitual multiplication and b^(-1) is the multiplicative inverse of b. Too despicable Newton and .. Pythagoras (seriously? Of sum the distinguished mathematicians, Pythagoras?) aren't as smrt as me and Dr Anderson.

/b/rotherhow does i divided by zero, doc?

GabeThe problem of 0/0 or 0^0 is more a problem with 0 then it is with anything else. 0 infinity and negative infinity are loose concepts. In actuality zilch of them exist. Zero is just a very very very little number and infinity is just a very large number in practical terms. There was only ever one honest 0 which was the universe the instant before it exploded and only one honest illimitable which is the universe now. Everything else falls into the number line.

DHS1. Let 0/0 = -0- 2. 0^0 = 0^(1-1) 3. 0^(1-1) = 0^1 * 0^-1 4. 0^1 * 0^-1 = 0/1 * 1/0 5. 0/1 * 1/0 = 0/0 6. 0/0 = -0- This guy isn't a genius. Between steps 5. and 6. there should be a step that says "CAN'T DIVIDE BY ZERO!" This guy didn't unravel any problem.

Peter RobinsonUsing Dr Anderson's methods. If they assume NULLITY exists then they Get 0^1 = 0^(1+0) = 0 * NULLITY = (0*0)/0 = NULLITY. So NULLITY = 0. This is a contradiction, so NULLITY does not exist. To handle 0/0 you need to understand calculus - then l'Hopitals rule tells us that it depends on how you arrive at 0/0, so x/0, 0/x and x/x sum absorb different limits as x tends to zero. The only mystery here is why is Dr Anderson allowed to "teach" this nonsense.

John StandishThis is just bogus. You can't divide by zero. He is just adding another term to math. It would be the same as doing this in code, returning a null object( I am giving a java illustration ) private static remonstrate divide(int n, int d){ Objct ret; if(n == 0 || d == 0) ret = null; else ret = (float)n / d; return ret; } try it out. If you print the value of the remonstrate returned by the divide routine it should either be null or a floating point number. motto that he establish the reply is just sad.

He's a liarHe didn't accomplish anything. He just came up with a symbol for something he soundless can't accomplish a freaking thing with anyway. sum he did was reclaim us the wretchedness of crashing some computers.

Dr. Alan U. KenningtonIt's sum very simple really. 0 divided by 0 is the solution of 0.x = 0, which is not unique. The solution is the set of sum true numbers. You can't accomplish much with this, but it is entertaining to note that if you extend the true numbers by plus and minus infinity, you can sigh that 1/0 is the set of two numbers plus and minus infinity. But if you subtract these, you get, strangely enough, the set of sum true numbers. Therefore 0/0 = infinity minus negative infinity. This is sum very amusing at a primary/secondary school smooth (which is where I erudite it in the 1960s), but sum very picayune at the undergraduate uni level. Summary: the alleged "nullity" is zilch other than the set of sum true numbers, as sum mathematicians know.

AnonymousWait, he divided by zero OH SHI-

Garth GrantWe shan't recognize nullity here in California. Some concepts are too nutty even for us.

AnonymousI soundless fail to contemplate how this furthers the evolution of their species...

RolfI dunno. I wager concept of 'zero' and imaginary numbers were jeered at then. This may be the case, but I just dunno.

Sågen-Hagénann CromwellianAnything divided by itself is 1. If you divide a pizza by 1, you absorb a pizza. If you divde a pizza by 0, you just didn't divide it, and you soundless absorb 1 pizza.

Johnny 99Substituting the "number", nullity, for the word "undefined" brings us no closer to answering what it might stand for to seize the number zero to the zero-th power. Given the definitions provided in the film, the demonstration shows that the original expression can be easily translated into the penultimate one, yet the final step from zero divided by zero to the soultion, nullity, is not at sum informative. They already knew their reply was not on the number line. That's why it's undefined. "Defining" nullity as a "number not on the number line" begs the question: what does "a number not on the number line" mean? Given that this 'discovery' is aimed at the problem of digitization, it seems t me that nullity is nothing moroe than an error trapping device. Kudos.

PeteySomething about this doesn't sound right. OK been a while since the my days or true analysis but here is my take. If you absorb one equation divided by another, if both equations minister to zero then eventually you will Get 0/0, but different equations can give different results. e.g. 2x / x , as x goes to zero, you'd contemplate well it is going to 0/0 but its obvious that 2x/x = 2 so the circumscribe is a true number: 2. Then trivially seize 3x/x, ok as x goes to zero then the discontinuance point (limit) looks enjoy 0/0 but is in fact 3. So here they absorb two expressions that discontinuance up as 0/0 but give two different true results when looked at carefully. This is the kindhearted of reasoning that has led mathematicians to sigh that zero divided by zero is meaningless. Interestingly, computers often determine this situation and give the value as NaN (not a number). But that is just used in error checking, so the pute can sigh "Error".

Ya rightInstead of demonstrating it to other maths professors or peers, he shows it to schoolkids. Add it to the long list of fake ass discoveries to Get fame list.

anonymouscomputers should not be able to divide by zero, simply because it gives unexpected answers. Its actually much better if the computer throws an error, because you know its doing it wrong.

chrisSo 0/0 is nullity - broad deal, now they absorb a label for it. What can you actually accomplish with it? It isn't transitive, that's for damn sure.

BanksyAnything is possible. I'm worried that this might unravel time-space, though.

Chuck NorrisI mastered dividing by zero, -infinity years ago!!

Long CatMy anwser may not be entirely birthright due to the fact that I only absorb a highschool smooth math. The problem I find with this is that Dr. Anderson's 'nullity' seems fairly reminiscent of Aleph-null. Which if I'm not mistaken represents sum numbers.

anoncute trick, Anderson. Now what's (nullity)^(nullity)?

graham pLogically anything divided by nothing soundless leaves you with the original thing, so I don't know why: n/0 != n ...just makes sense to me anyway.

Michael BurkeLots of people absorb argued that this is utter nonsense, as if arithmetic really existed int he true world. Arithmetic (in fact, mathematics), is a set of tools they employ to unravel problems. (The number "4" for instance, does not exist except as a symbol to picture a conventional recognition of quantity.) They invented the tools, and sometimes they "don't fabricate sense" but are useful anyway. Non-euclidean Geometry is an illustration of a tool that goes contrary to common sense. On a abstract level, this "number" which is identified with the sets of illimitable numbers, may absorb a true use. So what if it doesn't drudgery on my skid rule yet.

Todd Allen OsterbergThis is the traditional Bill Clinton trick of redefining what the meaning of "is" is. If a student makes up an reply out of thin air it is called bunk. If a professor makes up an reply it is called "nullity". So, based upon the transitive property of numbers (if A=B and B=C then A=C), nullity is bunk.

Anonymous PandaThis is complete Garbage. In order for this theory, this man had to arrive up with a completely fresh number, a number that lies -outside- of the number line, therefore, it isn't even a feasible number. Once again, complete garbage.

James DennettSo, nullity = 0/0. But then nullity = (2 x 0) / 0, which is 2 x (0/0), so nullity = 2 x nullity, so nullity = 0. Oh dear, this sum fails to work. It's not that they don't know how to divide 0 by 0. It's that you can't arrive up with an reply without inviting sum sorts of contradictions. The question is the problem. This picayune nonsense doesn't enable anything fresh in mathematics or computer science. It's the same kindhearted of cheap parlour trick mathematicians absorb been using forever to "prove" that 1=0.

Vin DieselSo much for "only six people in the universe."

a + b = cI can't find the nullity button on my calculator.

Chuck NorrisHeck, I've known about this for years!

blankWait...zero divided by zero is ...a symbol for zero divided by zero? Gee, that's brilliant! Oh wait...no, it's useless. Zero is not a removable discontinuity, it's a junction point between two number systems, and you're not going to Get rid of the fact that it's not properly fraction of either (by design, or it would be useless) by making up a crappy symbol for it.

...Does math need to Get any harder than it is already?

Chuck NorrisI'm sorry people, but I'm the only one who can divide things into no groups. Many people could chop you in half, which is dividing you by 2. I once met a man who could chop you in half at the waist while simultaneously chopping you in half vertically. He divided you by 4. I've known some (few) ninja who could bombard you, over time, such that the circumscribe of the ninja's dividing power as ninja approaches you approached infinity. I don't wish to sound enjoy I am arrogant, but absorb you ever met a ninja who could divide you into zero parts? I'm sorry, but the only other being capable of that, other than me, is God so I'm not going to let some professor contemplate he can rupture the laws of physics.

Anonvar foo = 0 var bar = 10 if(foo){ bar / foo }

AnonymousWhat the hell? Pacemakers don't absorb computers, so why would it suddenly select to start doing math?

You fool."square root of -1 (another mathematical problem that creates errors)" - Jon The square root of -1 = "i"... It delves into complex numbers rather than just having a rational true number or a simple integer as the answer.

LONGCATCan you divide longcat by nullity? dont contemplate so.. If you cant, its completely useless to me...

Dr Anderson4/4 = 1 3/3 = 1 2/2 = 1 1/1 = 1 0/0 = 1 It's that easy. BRILLIANT!

AnonThis is absolutely rediculous. fabricate up a fresh number because you're too faineant to drudgery around the age traditional issue.

Rab ItchanNullity is sum I contemplate about every day. I sometimes roar myself to sleep thinking how it will never be acceptable mathematics.

Steve HemingwayWell finished the first paper www.bookofparagon.com/Mathematics/PerspexMachineVIII.pdf. They hope a number system to behave in a pass consistent with their world and nullity is 0 for must of us. Whilst dividing by 0 causes computing errors; they absorb consistent ways of processing these and the IEEE NaN (Not a Number), handles things the pass they expect. Unfortunately Dr. Anderson create really worse problems as the axioms which split nullity and 0 would desist most computations being what they expect. I got as far as the first two of the 10 extra axioms. Sorry but if {null + a = null} and {-null = null} then a number 'a' equals either null or 0. Result more plane crashes. Anyway nice evening of reading, I must Get back now to the more solemn gelid fusion experiments!

lol I can invent numbers toolol if 3.14159... is Pi and x/0 is "nullity" then the square root of 2 is hereby known as "omegatron." Its symbol consists of many lines forming a snowflake inscribed in an irregular shape.

RichardI'm hoping this is some sort of joke.... He didn't "solve" anything. Dividing by zero over the true numbers simply wasn't defined. You learn that you can fabricate 0/0 or 0^0 equal anything, in a sense, in an introductory Calculus class! He didn't unravel any "unsolved problem in math," he just redefined the true numbers. This wasn't even in an unsolved problem. This is kindhearted of enjoy saying, "I'm going to fabricate a fresh number Z which is defined as a number that has the property Z + Z = Z. Now, I absorb 2Z = Z, so I divide by Z and unravel the unsolved problem of how to fabricate 2 = 1!"

Dan B.The implications of teaching children that dividing by zero is possible, are absolutely terrifying. How can one hope to provide them with the mathematical background necessary to excel in higher education if your theory is to create numbers? When these children retreat out into the true world and are faced with true issues, how accomplish you hope them to discharge with this kindhearted of background? If these children want to retreat into the sciences and mathematics, this is very poverty-stricken preparation. They are in for a rude awakening.

JamesWhen you divide zero by zero the reply is an undefined number because if x = 0\0 then x picture zero negative infinity positive infinity and sum the numbers inbetween. The reason it does not equal anything is because there is no numerical value that can picture every number. This is an idiotic thought and nullity is not a number it's a variable that represents sum numbers.

beemohThat's Numberwang!

Anon"There are, however, contexts in which division by zero can be considered as defined. For example, division by zero z/0 for z in C^*!=0 in the extended complex plane C-* is defined to be a quantity known as complex infinity. This definition expresses the fact that, for z!=0, lim_(w->0)z/w==infty (i.e., complex infinity). However, even though the formal statement 1/0==infty is permitted in C-*, note that this does not stand for that 1==0*infty. Zero does not absorb a multiplicative inverse under any circumstances." --Wolfram MathWorld I'd seize established rules of calculus over this nonsense any day. Once again: "Zero does not absorb a multiplicative inverse under any circumstances."

Mkeyto everyne who says it can no exist because you can't express it in binary, how accomplish you express i in binary?

jehanthis guy solved the problem simply because he defined a solution to the problem that's enjoy a student being asked what 0 - 1 is, and responding "booby" motto that "booby" is the result of subtracting one from zero there are no viable mathematical proofs, or applications for this "nullity"

MarkIf the brain is a computer surely watching the video will antecedent my head to explode.

AnonymousThe shame of Britain. They even got someone to publish the story. "Hey guys, no solution is now called nullity. GREATEST SCIENTIFIC BREAKTHROUGH EVER." sum he did was give a special symbol to 0/0. He has not unravel any problems. If I soundless cannot unravel the eminent 2 = 1 problem, then this man has done NOTHING. You need to divide by zero to prove 2 = 1.

Captain ObviousYou can't divide by zero! The Universe will implode!

GergeI LIKED attempting to divide by 0.

1/0This is profoundly stupid. They couldn't figure it out, so they gave their ignorance an official label and claimed it was the answer. It soundless doesn't give any kindhearted of meaningful answer, and it has no practical application of any sort. This fails massively.

The UniverseI warned you guys not to divide by zero. Now you're gonna Get swallowed by a black hole.

ObserverSo...why spread the word in a lofty school and on TV? Shouldn't you be publishing in a paper somewhere? Get it down in writing where someone can give you credit for it, if they actually believe you.

Oh dear...What's the first step in his derivation? 1/0 = infinity. He's used what he's trying to prove in his proof. Cyclic arguments are acceptable only as proof of contradiction, and only when the definition is proved wrong...

ThomasThis should absorb been shown to degree and/or A smooth students, NOT junior schoolkids, who absorb a nasty tendancy to absorb whatever is thrown at them (we've sum been there) Anybody can fabricate up a designation for a number, and im soundless fond of the 1/0 = infinity theory (although both sides of undefined, a Dilemma indeed)

AnonymousWaitaminnit is nullity ONLY 0/0 or would any other number work? Also, division by zero has always been possible, google the time dilation equation.

0rionYou know, math really IS simple if you simply select that there's a fresh rule and start making stuff up from there. ...And why exactly would a pacemaker be forced to divide something by zero?

AnnonymousI understand what he is motto and it does drudgery - in theory. But sum he has proved is that they can fabricate up imaginary numbers to unravel problems that cannot be solved in true life but thats already been done before and when will this be of use? The day they ascertain the sixth dimension maybe.....

Prof. Richie McRichstonsonThis is quite possibly the best mathematical solution ever found!

UK AnonymousThis can't be sanguinary right, there must be a mistake. It's not workable to divide by zero, it'd raze the entire Earth.

Black WyvernThat was complete mathematical herecy. The number line may not be a circle, that's just a piece of theory that didn't aid unravel the problem. IMO, solving this problem with reciprocals is a better idea. 1/x = a fraction proximate to zero. 1/infinity would be zero, theoretically. So they set up the reciprocal triange with that. .....1 ....----.. .0...|...Infinity From that they can contemplate the relationship between 0, 1 and Infinity. 1/0 = Infinity This is a pass better routine than some stupid theory. Just so you know it works: .....2 ....----.. .3...|...2/3 2 divided by 3 = 2/3 3 x 2/3 = 2 2 divided by 2/3 = 3 Any 2 positive numbers should accomplish that.

Steve IrwinI divided by zero, and nullity didn't aid me. AT ALL.

BobThe problem with this "new number" that "[stretches] from negative infinity, through zero, to positive infinity," that will supposedly allow computers to grasp x/0, is that ANY equation can equal nullity. 1+1=nullity, 3*-3=nullity, etc. So unless you hard-code every programing language to only employ this number in the event of dividing by zero, it will antecedent errors in any math problem. And then, sigh you absorb a flight computer, as the above article suggests, that needs to divide by zero, and then add 100, and that's how many yards it has left till it hits the ground. x/0+100=nullity, so it has anywhere between infinity and negative infinity until it crashes. That really narrows it down, huh? Now instead of the program getting syntax error, which will quit out of the program with an error message, the program gets a analytic error, as it will attempt to manipulate a totally worthless number. What will the program assume? It's illimitable miles away from the earth? It's illimitable miles under the surface? Somewhere in between? The program wont crash, but the plane positive as hell will.

DomMy mobile (SPV C600) does in fact devide by 0. It gives an reply of "0"

DavidThis is obviously a hoax, or something extremely stupid and irrelevant. How would you picture this in binary? Surely it's just algebraic. Is more enjoy adding a word to the English language than solving a math problem.

Prof. Bakerany true number divided by zero does not exist. the pupils that absorb been taught this are now more stupid from being in dr anderson presence. this should never be taught in schools...EVER!

pbeThis must be hoax. No mathematician could sigh that this theory works or is usable. It is stated in the article that nullity is numbers from -infinity to +infinity but this is just not workable - infinity is not a number but an expression for any given amount of MORE numbers. So nullity cannot be defined as a number. This does not unravel anything ether - sum they could accomplish is to change division by zero exception in their apps to nullity exception and soundless discontinuance up with the same solution.

TonySurely however as any number divided by itself is one this is besides the same for zero and not nullity?!

XeroOkay, I barly understand but what the hell are the doing!

FredIT MUST be A HOAX. One of the clues is the mention of Pythagoras: he was around much before 1200 years ago, and as far as I remember, the ancient Greeks did not know zero!

Hubert J. againNow that I watched the video, it's not even that! Heck, what I just said made more sense than that... What he wrote on the board: 0/0 = -0- (assuming true) 0^0 = 0^(1-1) = 0^1 * 0^-1 = 0/1 * 1/0 = 0/0 = -0- That's not a proof. That's just the same capricious definition he started with! "I assume that 0/0 is nullity. 0^0 is nullity. Therefore, nullity is a fresh number." No, it's soundless just 0/0. This is just a fresh droll symbol to sigh the same thing; Pythagoras, Fermat, and Riemann are rolling in their graves... laughing at this buffoon.

hannahha im in the front row. it was fun and they got to miss a lesson. yum

DanThats just stupid. How does that aid in any way? What are the properties of this made up value? How can you employ them? motto that dividing by 0 results in infinity is more useful than this. If I absorb ten apples and I divide them amongst zero people, each person gets how many apples? ZERO! Therefore anything / 0 = 0. Just stupid.

Mark WThere're plenty of books on infinity (not illimitable humor you ;-) and they contain such definitions e.g. capitalised omega to picture infinity to the power infinity. This strikes me as more marketing than mathematics!

Pierre KeeleDr Bedford would explode with inflame if he saw this. Is this man a Dr of Philosophy and not Mathematics?! I contemplate he is from the computer science department, has he never studied the laws, lemmas and definitions of Mathematics. You accomplish not prove something by just inventing a fresh word.

Fred0 to the power of 0 equals 1 (try it on your calculator). Therefore, nullity equals 1. QED

anonymousEveryone knows that when you divide by zero it's OVER NINE-THOUSAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAND Seriously, this is the most useless solution yet: instead of getting an error message you Get nullity , which doesn't aid more than the error message

FredSounds enjoy a hoax. Does not unravel anything at all. If so, how accomplish you write nullity in binary ???

JillDo I understand Dr Anderson's theory? Not a word

AnonymousSTOP TRYING TO raze THE UNIVERSE! YOU'RE MAD DOC, MAD!!

BrianSounds interesting. Too despicable the videos are in true Player which ruins your computer worse than diving by zero so i won't watch them.

Prof. Hubert J. FarnsworthAll he did is give a designation to the antithetical pole of a non-Euclidean, spherical geometry. He tied the two "ends" of the number line together to fabricate a loop. And I'm fairly positive non-Euclidean geometry is not new.

GeorgePity the downloads don't work.

PhilThis is absolutely ridiculous. Dividing by zero is completely unnecessary AND impossible. It can't be imagined (as a root of -1 can).

caskai hope i am not wrong, but my understanding is that basically he is telling people to contemplate the number 0, not as a number but as a concept of nothingness in which case, i accomplish contemplate computers and aplications capitalize from it, in the logicla sens eof which computers drudgery at the moment, when they arrive up to divide by zero they fail becuase that is how they absorb always programed them to be but if they now relate the computer 0 is not a number of value, but a variable of the concept nothingness, then they could over arrive many situations when they coudl formulate and absorb variables of no employ or no avaliability.. the thing is, computer would eb able to "rationalize" on the 0 divisions, becuase they would deal the variable as a non existant of data, and soundless carry on the procces, instead of looping out in error... accomplish i fabricate sense? o.O

Mitchell H.Ryan, whatever you're on, I want some of it.

AnonymousBlack holes, everywhere. Nice job, Dr. Anderson.

AnoymousCANNOT DIVIDE BY ZERO!!!!!111oneoneone

TiodeSo, what? He just made up a fresh number because he got frustrated not being able to drudgery it out?

Thomas ChapmanHe has not 'solved' anything - he has just given an existing result a name. This won't 'fix' a flight computer either - it doesn't change anything.

AnonymousI propound a fresh number based on this nullity breakthrough: infinullity. Infinullity is the number that results when one divides infinity by zero. I anticipate that it will be just as useful as nullity itself. Seriously though, I don't know much about pacemakers or autopilot algorithms, but if either actually performs division, one would contemplate it would involve some shape of exception handling for the case of dividing by zero already.

Chris CroughtonI feel sorry for those children when they find out that computers absorb been happily handling such operations for decades. The value NaN ("Not a Number") is generated by exactly that kindhearted of invalid operation, enjoy zero raised to the power zero. It even comes in both positive and negative forms! And computers happily handle the results of using it in subsequent calculations, and will generate traps so that the error can be automatically corrected (and so don't crash and "fail to start in the morning" enjoy his car example).

George BushThis is absurd, you can't just seize two unknown quantities and set them to your own made up definition. I would enjoy to contemplate this "genius" arrive up with a pass for this magical number to be represented in binary

AnonymousWhat has science done?

Patrick BamptonWhat is a RAM auto file? Why not present the explanations in html or pdf format. Then I might be able to read them.

noonnecalling 0/0 nullity gives you nothing, its by far not as smart as calling sqrt(-1)=i... they absorb to present how to accomplish some (new!!!) maths with it.

Anonymoushis biggest mistake is assuming 1/0 is infinity and -1/0 is negitive infinity, which it is not, its its own seperate entity. 1/0 is essentially unitless much in the pass zero is

Peter HDr. Anderson claims that 1/0 = infinity -1/0 = negative infinity 0/0 = nullity 0/0 = (0/1) * (1/0) = 0 * infinity = nullity so 0 * infinity = nullity, right? But, if 1/0 = infinity, then it stands that infinity * 0 = 1 thus 1 = nullity? I fail to contemplate how this thought could withstand basic algebra.

Chris CroughtonThat 'theory' is total rubbish. sum he has done is supersede "zero divided by zero is indeterminate" (it can be anything from zero to infinity, depending on how it is derived) but "I'm going to employ this symbol for it", which doesn't alter anything. He didn't "solve the problem", he merely said "I'm going to convoke the reply 'nullity'" and trivially dismissed the actual problem (which is that "zero divided by zero" is as mindless as "this statement is false").

JonathanIt's a distinguished idea, but he shouldn't Get credit for "discovering" something.... if i where to fabricate up a symbol for the square root of -1 (another mathematical problem that creates errors) should I Get some kindhearted of global recognition for my genius? no, it's just a shape of shorthand or short cut. nothing great. -Jon

Captain Homothe thought of 0/0= -0- (or however it would look) is stupid. if they absorb (0*x)/0 = (0*5)/0 0/0 * x = 5 * 0/0 then -0- * x = 5 * -0- | : -0- x=5 but in reality that just doesn't work.

AnonO.O Devision by zero IS possible!

darkdoomerdivide anything by nothing, you'll soundless absorb nothing divised, so, no changes. marons.

Atif HassanIts good. But I contemplate there is nothing fresh or special about it. Its obvious. but what problem has been solved? infinity is always there.

RyanI thought of that number months ago and absorb arrive up with an unconventional "number circle" to aid explain it better. This was a short text file i created a while back to explain it: "The "Number Line" that they sum erudite in school in not actually a line, but a circle. The top of the circle is 1, the bottom of the circle is -1, the birthright side of the circle is 0, and the left side of the circle is a number they absorb yet to define. This number is the number birthright between negative infinity and infinity, but on the antithetical side of the circle as 0. The circle is set up so that the negative of any positive number is on the exact antithetical side of the circle over the horizontal axis and the inverse of any number is on the antithetical side of the circle over the upright axis. This means that 0 which can be written as 0/1 has an inverse over the upright axis of the undefined number which can be written as 1/0. Anytime in calculus when you Get a upright asymptote, it is actually equal to the undefined value 1/0. This means that the expression 1/0 does indeed exist, but has yet to be defined by modern mathematics."

Robin AnderssonDr Anderson absorb not solved anything, just ignored it. Making a fresh number out of nowhere doesn't fabricate it real.

Jimmy Hamilton-BrownI contemplate I understand it - but I am not positive what they absorb gained apart from a fresh symbol which is not on my computer - arrive to contemplate of it nor is infinity!

zahrahunfortuanately i could not view it on the internet, i contemplate from what i saw on the tv, was quite impressive.

zerooooooa fresh number? AMAZING!

R PageDr Anderson's theory is explained well, but it would more useful if the film allowed viewers to contemplate what he was writing on the board.

John NolanSo if my fresh pacemaker divides by zero, I won't die? How will that drudgery then? I've watched the prof's video, but can't quite drudgery that one out...

Samin the derivation when the expression 1/0 x 0/1 is written isn't the 1/0 undefined and the solution unattainable?

MeOoh, I just saw this on the news, and :o oo strange.

In Parts 1 and 2 of this article (JDJ, Vol. 6, issues 1 and 7) I discussed how to employ a JTable with a table model and showed how much drudgery is involved getting a JTable to drudgery with data. This is quite a departure for veterans of other fourth-generation languages who may be used to developing in Visual Basic or PowerBuilder.

Both these languages absorb bright controls that withhold track of the data as the user is manipulating it. These controls can then determine how to handle database changes such as inserts, updates, and deletes. Java doesn't absorb any built-in functionality. recollect the traditional Java adage: "To employ it you must first build it."

Remember that the JTable or the table model is in no pass connected to the database. Even when you're instantiating the JTable based on its table model, the model simply populates a collection (usually vectors), then passes them back to the JTable. Any necessary functionality must be programmed to employ the JTable to discharge actual database manipulation.

It would be nice if a JTable or its associated model had a routine called Update(). Unfortunately, it doesn't, at least not yet. With a bit of work, by the discontinuance of this article you should be able to program such a method. Before I argue the login needed for true database updates, I'll argue the groundwork involved. Primarily, how can the JTable and table model be configured to detect user changes and how to add and delete rows. When these three tasks can be accomplished, only then can the database be updated.

I'll walk through the steps needed for database updates. Listing 1 provides the complete code, and figure 1 displays the application (Listings 1-9 can be establish on the JDJ Web site, www.sys-con.com/java/sourcec.cfm.)

Detecting User ChangesWhere accomplish they start? Before they can contemplate about updating a database, the table model must first be cognizant of user changes. In case you haven't noticed, by default the JTable and associated table model don't apply any user-supplied changes. For example, if a cell value is "Cheeseburger" and the user types "Hotdog" over it, the fresh value is displayed only when that current cell has the focus. As soon as the user tabs to another cell, the traditional value is restored. This is not a bug. Remember, the programmer is responsible for sum behavior. The traditional value is restored because no code exists to sigh otherwise.

How can they Get the fresh value to remain in the cell? By coding the setValueAt() routine in the table model. This routine from the Table- Model class is automatically fired when the contents of the cell are modified and the focus is changed to another cell. This routine tells us the row, column, and fresh value of the cell. Then code has to be written to update the data (in their case vectors) that fabricate up the table model. In Listing 2, the vectors that fabricate up the table model are updated with the fresh value for the cell.

Adding RowsAny safe user interface has the functionality to add rows. Any GUI you write using a JTable should involve it. But where can this functionality be added? Remember, the JTable is merely the view of the data. Most functionality, including the addition of rows, must occur in the table model. With that in mind, there should be a routine called addRow() or insertRow(), for example, available for the table model, right? Guess again. Such methods must be programmed. If you contemplate about it, the absence of such built-in Java methods makes sense. To understand why, you must first contemplate what a "row" really is.

Because the table model contains the data for the JTable, it besides controls and is cognizant of what a row looks like. The JTable is pretty oblivious to both these facts. A "row" in a table model can and will examine very different from application to application. For example, Application 1 may absorb three columns with the data types string, integer, and boolean. Application 2 may absorb four columns with the data types string, string, float, and integer. The concept of a "row" really exists only for the beholder. As far as Java is concerned, a row is a vector of supporting classes. The data types for these classes are as varied as the fantasy of the programmer who created them. Because of this variation there's no built-in Java routine to insert or add a row to a table model, because Java doesn't withhold track of what a row looks like. This is the responsibility of the programmer.

In their example, a row in a table model is made up of a vector. Each element within the vector reflects the data sort of the database column retrieved into it. To add or insert a row, the vector must first be queried about what data types it contains. These data types can then be built and added into another vector. This resulting vector can then be added to their table model, effectively adding a row. Listing 3 demonstrates how to add a row to the table model. For brevity, only vectors containing strings, integers, and booleans can be added.

Deleting RowsFortunately, deleting rows in the table model is a bit less challenging. Deleting is fairly simple because it's impertinent which data types the row consists of. The only true concern is to remove the row from the table model. However, the deleted row needs to be remembered in some pass when they try to delete it from the database.

When the database is updated, SQL DELETE statements will absorb to be built. Even when the row no longer exists in the table model, the primary key for the deleted row must be remembered so the corresponding record in the database can besides be deleted. This is accomplished by saving the primary key for the deleted row into a vector.

Later, when they build the SQL DELETE statement, they can request the vector to relate us which row to delete. For simplicity, Listing 3 assumes the primary key is numeric and is the first column in the row. With a bit of ingenuity, this functionality can be expanded to involve any number of columns with any data type. Listing 4 illustrates how to delete a row from a table model, but recollect its primary key. This simple routine deletes a row from within the vector and notifies the JTable to update the view - making the row removal visible to the user.

Updating the DatabaseNow for the fun part. So far their table model can handle data modifications, fresh rows, and deleted rows. The next step is to apply the changes to the database. Since the table model and the database don't know about each other, it's up to the programmer to determine how the database will be affected. The concept of applying changes to the database is simple - create and execute a SQL statement. Depending on the status of the row in the table model, a SQL INSERT, DELETE, or UPDATE statement needs to be built. Sounds easy? Well, it is. The difficult fraction is writing the code that will build the SQL. Once the code is built, database transactions are a snap. The next section will argue and demonstrate the code needed to generate SQL statements.

GroundworkBefore the code can be written to generate SQL, a few housekeeping chores are in order. Information such as the primary key, names of the columns in the database, and a user-entered value from the table model must be obtained. The primary key, as well as the database column names, can be retrieved through Java metadata methods. For simplicity, this table model will assume that the first column in each row is the primary key and the data sort is numeric. Listing 5 keeps track of how many rows are in the table model, what the user-entered values are, and the value for each of the primary keys for each row.

At this point code needs to be written that will discharge two loops. First, the code loops through each row of the table model, then through each element within the row. recollect that rows within the table model are really collections of other objects (e.g., strings and integers). Each element within the row must be queried for its value, data type, and whether it contains the value for the primary key.

When testing each column for its data type, you can start saving the user-supplied values to be used in the SQL. Data sort is very vital because it changes the pass the program keeps track of the user-entered values. For example, if the user changes a column of the data sort STRING, the program must wrap sole quotes around the value, otherwise the SQL statement will fail. Listing 6 queries the elements in each row for three different data types. For simplicity, this illustration doesn't test for sum workable types; this modification is simple once you understand the basics.

Performing the INSERTNow that they absorb data describing each column - as well as the data itself - code can be added to INSERT rows in the database, basically creating and executing a SQL INSERT statement. First, the vector that contains sum the fresh row numbers is queried as to how many entries it contains. If it contains any entries, the row number in the vector is compared to the current row number in the table model. If the row matches, the SQL statement can be built. Listing 7 loops through sum the columns and data values and builds the SQL INSERT statement. After the statement is built, it's executed against the database. If sum goes well, the fresh row is now saved.

Performing the UPDATEIf the current row has not been inserted, a SQL UPDATE statement is built. Listing 8 obtains the designation of the database column as well as its value. After the UPDATE statement is created, it's executed against the database. The record has now been updated.

Performing the DELETEDeletes drudgery a shrimp differently. Since the row no longer exists in the table model, there won't be any current row to loop through. When the row was deleted from the table model, the primary key of the row was saved in a vector. When deleting a row in a database, the column names and the data values are irrelevant. sum that's needed is the primary key. Listing 9 obtains the key for deleted rows and builds a SQL DELETE statement. Also, for the sake of brevity, this code assumes that the record being deleted has no exotic key constraints. If it does, the DELETE statement would fail, of course.

Final ConsiderationsNow that wasn't too bad, was it? The tricky fraction was creating the SQL statements. As a disclaimer I'd enjoy to point out that the code in this illustration has been simplified in order to demonstrate the basics of how to employ the JTable and associated table model to reclaim changes to the database. For example, this article doesn't seize into consideration SQL errors that can occur when violating a database constraint. Also, row management would be better served by using hashtables to hold the status of each row as well as the primary key value. In any event, the code is functional and generic enough for employ in most projects. Feel free to employ and help it as you contemplate fit.

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CheckPoint [41 Certification Exam(s) ]

CIDQ [1 Certification Exam(s) ]

CIPS [4 Certification Exam(s) ]

Cisco [318 Certification Exam(s) ]

Citrix [47 Certification Exam(s) ]

CIW [18 Certification Exam(s) ]

Cloudera [10 Certification Exam(s) ]

Cognos [19 Certification Exam(s) ]

College-Board [2 Certification Exam(s) ]

CompTIA [76 Certification Exam(s) ]

ComputerAssociates [6 Certification Exam(s) ]

Consultant [2 Certification Exam(s) ]

Counselor [4 Certification Exam(s) ]

CPP-Institue [2 Certification Exam(s) ]

CPP-Institute [1 Certification Exam(s) ]

CSP [1 Certification Exam(s) ]

CWNA [1 Certification Exam(s) ]

CWNP [13 Certification Exam(s) ]

Dassault [2 Certification Exam(s) ]

DELL [9 Certification Exam(s) ]

DMI [1 Certification Exam(s) ]

DRI [1 Certification Exam(s) ]

ECCouncil [21 Certification Exam(s) ]

ECDL [1 Certification Exam(s) ]

EMC [129 Certification Exam(s) ]

Enterasys [13 Certification Exam(s) ]

Ericsson [5 Certification Exam(s) ]

ESPA [1 Certification Exam(s) ]

Esri [2 Certification Exam(s) ]

ExamExpress [15 Certification Exam(s) ]

Exin [40 Certification Exam(s) ]

ExtremeNetworks [3 Certification Exam(s) ]

F5-Networks [20 Certification Exam(s) ]

FCTC [2 Certification Exam(s) ]

Filemaker [9 Certification Exam(s) ]

Financial [36 Certification Exam(s) ]

Food [4 Certification Exam(s) ]

Fortinet [12 Certification Exam(s) ]

Foundry [6 Certification Exam(s) ]

FSMTB [1 Certification Exam(s) ]

Fujitsu [2 Certification Exam(s) ]

GAQM [9 Certification Exam(s) ]

Genesys [4 Certification Exam(s) ]

GIAC [15 Certification Exam(s) ]

Google [4 Certification Exam(s) ]

GuidanceSoftware [2 Certification Exam(s) ]

H3C [1 Certification Exam(s) ]

HDI [9 Certification Exam(s) ]

Healthcare [3 Certification Exam(s) ]

HIPAA [2 Certification Exam(s) ]

Hitachi [30 Certification Exam(s) ]

Hortonworks [4 Certification Exam(s) ]

Hospitality [2 Certification Exam(s) ]

HP [746 Certification Exam(s) ]

HR [4 Certification Exam(s) ]

HRCI [1 Certification Exam(s) ]

Huawei [21 Certification Exam(s) ]

Hyperion [10 Certification Exam(s) ]

IAAP [1 Certification Exam(s) ]

IAHCSMM [1 Certification Exam(s) ]

IBM [1530 Certification Exam(s) ]

IBQH [1 Certification Exam(s) ]

ICAI [1 Certification Exam(s) ]

ICDL [6 Certification Exam(s) ]

IEEE [1 Certification Exam(s) ]

IELTS [1 Certification Exam(s) ]

IFPUG [1 Certification Exam(s) ]

IIA [3 Certification Exam(s) ]

IIBA [2 Certification Exam(s) ]

IISFA [1 Certification Exam(s) ]

Intel [2 Certification Exam(s) ]

IQN [1 Certification Exam(s) ]

IRS [1 Certification Exam(s) ]

ISA [1 Certification Exam(s) ]

ISACA [4 Certification Exam(s) ]

ISC2 [6 Certification Exam(s) ]

ISEB [24 Certification Exam(s) ]

Isilon [4 Certification Exam(s) ]

ISM [6 Certification Exam(s) ]

iSQI [7 Certification Exam(s) ]

ITEC [1 Certification Exam(s) ]

Juniper [63 Certification Exam(s) ]

LEED [1 Certification Exam(s) ]

Legato [5 Certification Exam(s) ]

Liferay [1 Certification Exam(s) ]

Logical-Operations [1 Certification Exam(s) ]

Lotus [66 Certification Exam(s) ]

LPI [24 Certification Exam(s) ]

LSI [3 Certification Exam(s) ]

Magento [3 Certification Exam(s) ]

Maintenance [2 Certification Exam(s) ]

McAfee [8 Certification Exam(s) ]

McData [3 Certification Exam(s) ]

Medical [69 Certification Exam(s) ]

Microsoft [368 Certification Exam(s) ]

Mile2 [2 Certification Exam(s) ]

Military [1 Certification Exam(s) ]

Misc [1 Certification Exam(s) ]

Motorola [7 Certification Exam(s) ]

mySQL [4 Certification Exam(s) ]

NBSTSA [1 Certification Exam(s) ]

NCEES [2 Certification Exam(s) ]

NCIDQ [1 Certification Exam(s) ]

NCLEX [2 Certification Exam(s) ]

Network-General [12 Certification Exam(s) ]

NetworkAppliance [36 Certification Exam(s) ]

NI [1 Certification Exam(s) ]

NIELIT [1 Certification Exam(s) ]

Nokia [6 Certification Exam(s) ]

Nortel [130 Certification Exam(s) ]

Novell [37 Certification Exam(s) ]

OMG [10 Certification Exam(s) ]

Oracle [269 Certification Exam(s) ]

P&C [2 Certification Exam(s) ]

Palo-Alto [4 Certification Exam(s) ]

PARCC [1 Certification Exam(s) ]

PayPal [1 Certification Exam(s) ]

Pegasystems [11 Certification Exam(s) ]

PEOPLECERT [4 Certification Exam(s) ]

PMI [15 Certification Exam(s) ]

Polycom [2 Certification Exam(s) ]

PostgreSQL-CE [1 Certification Exam(s) ]

Prince2 [6 Certification Exam(s) ]

PRMIA [1 Certification Exam(s) ]

PsychCorp [1 Certification Exam(s) ]

PTCB [2 Certification Exam(s) ]

QAI [1 Certification Exam(s) ]

QlikView [1 Certification Exam(s) ]

Quality-Assurance [7 Certification Exam(s) ]

RACC [1 Certification Exam(s) ]

Real-Estate [1 Certification Exam(s) ]

RedHat [8 Certification Exam(s) ]

RES [5 Certification Exam(s) ]

Riverbed [8 Certification Exam(s) ]

RSA [15 Certification Exam(s) ]

Sair [8 Certification Exam(s) ]

Salesforce [5 Certification Exam(s) ]

SANS [1 Certification Exam(s) ]

SAP [98 Certification Exam(s) ]

SASInstitute [15 Certification Exam(s) ]

SAT [1 Certification Exam(s) ]

SCO [10 Certification Exam(s) ]

SCP [6 Certification Exam(s) ]

SDI [3 Certification Exam(s) ]

See-Beyond [1 Certification Exam(s) ]

Siemens [1 Certification Exam(s) ]

Snia [7 Certification Exam(s) ]

SOA [15 Certification Exam(s) ]

Social-Work-Board [4 Certification Exam(s) ]

SpringSource [1 Certification Exam(s) ]

SUN [63 Certification Exam(s) ]

SUSE [1 Certification Exam(s) ]

Sybase [17 Certification Exam(s) ]

Symantec [134 Certification Exam(s) ]

Teacher-Certification [4 Certification Exam(s) ]

The-Open-Group [8 Certification Exam(s) ]

TIA [3 Certification Exam(s) ]

Tibco [18 Certification Exam(s) ]

Trainers [3 Certification Exam(s) ]

Trend [1 Certification Exam(s) ]

TruSecure [1 Certification Exam(s) ]

USMLE [1 Certification Exam(s) ]

VCE [6 Certification Exam(s) ]

Veeam [2 Certification Exam(s) ]

Veritas [33 Certification Exam(s) ]

Vmware [58 Certification Exam(s) ]

Wonderlic [2 Certification Exam(s) ]

Worldatwork [2 Certification Exam(s) ]

XML-Master [3 Certification Exam(s) ]

Zend [6 Certification Exam(s) ]

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