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Professor Comes Up With a Way to Divide by Zero
54mc writes "The BBC reports that Dr. James Anderson, of the University of Reading, has finally conquered the problem of dividing by zero. His new number, which he calls "nullity" solves the 1200 year old problem that niether Newton nor Pythagoras could solve, the problem of zero to the zero power. Story features video (Real Player only) of Dr. Anderson explaining the "simple" concept."
So much for my $200 calculator.
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His new number, which he calls "nullity"
:-)
Well, thats just nullty.
Seriously though, as I understand it, this is simply another mathematical structure that allows a different scalar much like a real projective line, right? If that is the case, then there is nothing really new here and there can be no application or definition with real numbers or integers. Alternatively by interpreting this as a commutative ring, one might be able to extend this to where division by zero does not always get you in trouble, but the precise interpretation of "division" is fundamentally altered. This too is not a new concept.
However, all of that said, I am a bioscientist and my math skills are not as strong as a formally trained mathematician, so I will defer to those here who are stronger mathematicians than I if this interpretation is incorrect.
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ah no, not the same thing. With databases, it means unknown.
Well, maybe it's the same thing. I didn't read the article.
The professors at 'Rithmetic State were non-plussed upon hearing the news.
Is it just me or does it sound like he thinks he's invented the NaN?
There's zero comments yet. Wonder how many comments that is per poster
Has Netcraft confirmed it?
Anyone have a link to the Youtube or Gootube version of this?
I can make up numbers too...
What he did was assign the previously "undefined" integer with a defined symbol that means the same thing. Infinity in both directions.
While interesting, the concept has little use.
From the article "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 big trouble. If your heart pacemaker divides by zero, you're dead.".
Now, instead of getting an error message, the computer give a 0 with a line through it, and THEN an error message.
--sig fault--
So dividing by zero warps you from the regular number line to an alternate (nullity) number line. Does this make any sense to anyone?
mod original post up by 0/0 points :)
-- "Genius is 1% inspiration and 99% perspiration" - TAE --
At least it was last time I tried it.
-NaN
He just created a new model, a new rule set, a new abstraction of math to deal with the case of "x/0". In general, dividing by zero is bad for most algorithms. I mean, from a CPU's perspective, I don't see how adding any additional hardware would help.
Only Chuck Norris can divide by zero.
The article and Slashdot's synopsis don't make note of it, but Dr. Anderson isn't claiming to have discovered something new in dividing any number other than zero by itself. The video linked in the article shows him saying that 1/0 = infinity, and -1/0 = -infinity, but 0/0 = capital phi (nullity -- we'll ignore the fact that this usually means the golden ratio in mathematics). Math isn't my area of study so I don't know why 0/0 specifically is so important... the article certainly is very much a fluff piece. Anyone feel like explaining the importance of 0/0?
Correction: capital phi is flux (physics), lowercase phi is the golden ratio. Among other things. Oops...
Last time I checked, the limit of 1/x for all x positive as x goes to zero is......infinity. The simplest solution to most limits is to substitute the limit, in this case 0, into the problem. As you can see, 1/0 would render, by the professor's solution nullity, which is inconsistent with infinity. Multiplicity of representations should all yield the same results, it is a foundation of mathematics, add 1 to both sides of the equation, and you still have the same answer. Draw your own conclusions.
Wow, since this guy is a computer science prof, maybe he can come up with some value or symbol to represent "nullity." I suggest "NaN" for "not a number." (ducks to avoid rotten tomatoes)
Dividing by zero is not a "problem". It's just IMPOSSIBLE due to the way we structure our species' math. If you want to restructure our math as we know it (which he basically does by inventing his own false reality, so to speak), then you're not solving any problems. You're just being clever, and designing another system.. which has been done hundreds of times.
As I heard at one math forumn at the local university years ago, generations of mathematicians will be rising up from their graves, wracking their ancient canes against the tombstones, all screaming: "How dare you defy hundreds of years of tradition with this gabarage!"
(These old folks know how to scream!)
He's just renamed 'undefined' 'nullity' as if it's some sort of new concept highschool math geeks haven't thoroughly discussed.
I am a science fantasy fan
This is computer programming ABC: you DONT allow undefined behavious to occur in your program! (especially if your doing MIL-STD Ada for avionics etc.) This guys 'method' is just a form of exception handling that any programmer with half-a-brain could implement.
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"... solves the 1200 year old problem that niether Newton nor Pythagoras could solve ..."
This is a joke or they don't know what they're talking about--Pythagoras lived roughly 2500 years ago.
Yet Another NaN? ;)
--I thought I was wrong once, but I was mistaken.
..is going to need a new handle.
It's sad that he teaches math and thinks this is a worthwhile concept.
For just one example of why it sucks, he BEGINS by defining: (infinity) = 1/0 and (-infinity) = -1/0.
My conclusion: (0)*(infinity)=1
So 2*0*infinity = 2*1
So 2 = 2*0*infinity = (2*0)*infinity = 0*infinity = 1
And once you know that 2 != 1 and 2 =1, it turns out you can prove quite a bit...
Total nonsense, and the BBC is encouraging it. *shakes head* Although, I've got to say, it's nice, for once in my life, to deservedly be a smug American.
Think! It ain't illegal yet!
George Clinton
Just tell me what is to happen If I were to divide 5 apples among 0 kids.
Now I am the last person that should be replying to you, and I'm wasted so it makes it even worse :/, but AFAIK imaginary numbers are considered "satisfactory" because during certain situations they can cancel each other other, therefore the "imaginary" equation becomes a real value. Once again it's been like 5 1/2 years since I've done math so.... (grain of salt)
Uh... are you joking?
Imaginary numbers (specifically, complex numbers, which consist of a sum of a real and an imaginary number, and which comprise the "complex plane") are INCREDIBLY important in the "real world."
I'm just a chemist, not a mathematician, but I am well aware that imaginary numbers are critical in the Fourier transforms used every time I take an IR or NMR spectrum.
Ever do electrical engineering? Circuit analysis is made a great deal easier when you can treat circuit elements in terms of complex numbers. All that "impedance" stuff you hear about capacitors and the like that makes it possible to apply Ohm's Law to LRC circuits.
These also are not merely made up properties, they are fundamental to mathematics and thus (if one believes that math is the language of the universe) physics. For example, certain integrals necessarily yield imaginary results. These integrals are not of some ethereal interest, but appear throughout quantum mechanics. This is why the amplitude of a wavefunction (used, for example, in molecular modeling that allows for practical achievements like better medicines) is not the square of the wave function (or, for that matter, its absolute value) but the product of the wavefunction and ITS COMPLEX CONJUGATE.
If you'd like more examples of the utility of complex numbers and other "random rules," check out Boas' "Mathematical Methods In The Physical Sciences."
Now I can carry out my big plan to fix the budget and trade deficit, make Pluto a planet again, and store a black hole in my garage fridge.
Table-ized A.I.
I'm not a math-pro either, but just an idea.... If you divide any number (except 0), by zero you can take the limit of either side and you get -Inf or +Inf. Now, keep in mind that 0 divided by any number (except 0) is always 0: f(x)= x/0 = 0 (x element of R\{0}).
Now combine the two... By using the first statement (using limits), the result of 0/0 should be either -Inf or +Inf. By using the second statement the result should be 0... Somehow, thus, 0/0 should be -Inf, +Inf and 0 at once. Not that I see that as a problem, but hey, as I said: IANAMathematician.
1... 2... 3... Ah, there, is the mathematician with the Clueb *Ouch!* ;-)
Ahhh...the great dumpster continuum. Many a free computer will be found there. -- sowth (748135)
Helpful little hint from the end of the video:
Yeah. It was that simple.
I'm just reminded of that proof from way-back-when that 2 = 1:
All this guy has done is provide another little fun "proof" that you can use to win bar bets. "Betcha I can divide by zero..."
The heavens do not fall for such a trifle.
In my Graphics class I learned about the Quaternion number field, which is essentially like multidimensional complex (real +imaginary) numbers. In addition to the familiar i, you also have j and k. There is a multiplication table showing what you get when you multiply these things with each other. Why are these useful? Because for some reason or other, they can be used to define 3D rotations "better" than just using two or three angles. And you can make quaternion splines to interpolate between various rotations, allowing you to specify key frames and getting an animation out of it. But it's a really weird sort of number to think about.
yea, actually, you are missing the point.
math is actually the science of making up rules. any real mathematician will tell you that the main idea of math is to start with as few basic axioms as possible, and come up with the rules of the system that follows. see: euclidean geometry, arithmetic. where do the axioms come from? historically, from observing the real world, people saw integers, real numbers, and euclidean geometry. more recently (meaning euclid and a few other clever early dudes, but otherwise in the last 150, maybe 200 years), the axioms are pretty much completely made up. some of them are based on those early systems, integers and real numbers. but there are a multitude of mathematical systems, of all varieties, that have no real world counterpart. and thats what makes it fun.
as for division by zero, it gets us nowhere. the system of arithmetic and real numbers doesn't define division by zero, because that system is used for modeling the real world, where division by zero is meaningless. if you paid attention to the paragraph above, however, you should realize how easy it is to come up with a system where division by zero is clearly defined. my favorite example is the riemann sphere, which can be seen as an extension of the projective real line. of course, in ieee floating point, division by zero is very clearly defined. the result doesn't have a "value" but you can do it, and if you do, your plane doesnt crash.
in short, james anderson is an idiot. yes, i am basing this on my reading of the summary and (pointlessly vacuous) article. if only the video explanation weren't real format...
This seems to be as useful to a physicist as imaginary number. It may come up in calculations and solutions but any physicist would be laugh out of the conference room if ever equated a measureable quantity to an number with imaginary component. The problem lies in the fact that nullity lacks a physical analog. Call 0/0 anything you want but in the end it useless without knowingwhat a nullity of anything represents. Thank you for participating. NEXT!!!!
You don't have to be smart to use a Mac, you just have to be smart enough to buy one
Mr. L'Hopital would have something to say against this.
Unfortunately I don't have Real installed to watch this nullity explanation, but I think you're way off base with "imaginary" (now, better known as "complex") numbers. Being able to do math with complex numbers is one of the major reasons all those electrical circuits in your computer and home work. it's a logical construct and has significant practical purpose. As for nullity? Who knows.
Btw, am I the only person who thinks that a pacemaker or any kind of truly mission critical device that "attempts to divide by zero" will not "simply crash?" You'd figure there would be some kind of failsafe in the code that goes at least a step beyond the old B-Movie "THIS DOES NOT COMPUTE...OVERLOAD! OVERLOAD! ARGHHHH...."
I hate to put it this way, but "It'll make sense when you're older". And by older, I mean when you take a higher math course. What is the square root of -1 equal to then? Nothing? Something? Saying it's "imaginary" is merely a construct that allows us to muck with things. We could say they're "happy fun times" numbers, with the symbol "hft", and it'd mean the same thing.
Seriously, in elementary school a teacher of mine tried to tell us that 1/0 = infinity
Read up on the definition of division. If for a moment we ignore the "and the divisor is not 0" part of the definition, one of the basic principles of division is:
if a * b = c
then a / c = b, and b / c = a
A fundamental part of his explanation pivots on the following being true:
1/0 = infinity
-1/0 = -infinity
So, according to that, the following would hold:
if 1/0 = infinity
then infinity * 0 = 1
which does not work, for obvious reasons. This I told my teacher in 6th grade.
The real idea is that, for an equation 1/x = y, y approaches infinity as x approaches 0. At x=0, y is undefined, and that's all there is to it.
Secondly, the story promises one thing, and "delivers" another. It promises to tell you how to divide by 0, and instead tells you how to get 0^0 (which is based on the previously mentioned false premises). And the answer he gives on how to divide by 0 is that the answer is infinity, which it isn't! I'd fire the professor that has the gall of teaching this to kids (after probably being laughed out by his colleagues).
Because mathematics doesn't deal with the real world. Physics does.
People take mathematical tools and models and apply them to the real world because they are useful. However, that usefulness is a lucky accident.
"Software is too expensive to build cheaply"
nullity: The ratio of women this guy has had in his bedroom to the number who slept with him.
No math teacher would ever refer to positive and minus infinity.
Last updated 6/12/2006, so not only is this story completly worthless (as anyone who even remotley understood Calc 1 could tell you), but it's 6 months old. Good job slashdot!
I am the first to admit math has NEVER been my strong suit
Yeah?
My computer divides with 0 just fine.
> 1/0
inf
> atan(1/0)*180/pi
90
I discovered that by accident - wrote a little 3D game, and after getting it to work, it occured to me that walking straight to the east (i.e. 90 degrees) would give me a direction vector of (1,0), which would then make the game calculate 1/0 to find out the angle. Huh? Why doesn't it crash? Let me just try a little test... atan(1/0)*180/pi (the *180/pi part is to get degrees): 90 degrees. So not only does it divide by zero just fine, it even does further calculations on the result, coming up with the correct angle.
Anyway, some people have mentioned that he probably didn't invent inf, but NaN. Nothing new about that either, but NaN does not allow further calculations (the result stays NaN), as the value as NaN is really undefined (where as inf has a defined (albeit abstract) value). Because x/x = 1, and 0/x = 0, the case of x=0 would give 0/0 = 0 and 1 at the same time. Can't do further calculations on that. So, basically he didn't invent any new math, he just came up with a new symbol for NaN. And started teaching it at a lower grade than usual.
Now, where is the "news for nerds" part? I would assume that most "nerds" are a least a little bit of math geeks, and thus, someone "inventing" NaN shouldn't be news at all.
Anyone feel like explaining the importance of 0/0?
It's what math professors think about when they're too old to bonk a student during those intense one-on-one tutoring sessions.
Note: IAAM(athematician). You pose a good question. The game in mathematics, though, is not to "make up random rules so that something that occurs to them suddenly works". It's (broadly speaking) to make up new rules which are completely consistent with all the old rules which allow us to understand a previously mysterious example. This is where "imaginary" numbers succeed tremendously, and "nullity" fails miserably. See my post downthread for why nullity sucks.
"Imaginary" numbers are just the "thingys" which are solutions to polynomials. I.e., mathematicians find it useful to have an answer to the question "for what values of x does x^2 + 1 = 0?" The answers are useful, even though they aren't good at measuring length or breadth or depth or other one-dimensional concepts. They're useful because they allow mathematicians to develop a theory which has answered questions which couldn't be answered before. This is true even though both the question and the answer both lie in the realm of real numbers. Should there be an answer to every question of this type that doesn't use complex numbers? Perhaps, but it certainly doesn't have to be pretty, or easy to discover. Often the shortest path to a "real" truth lies on an "imaginary" line.
Think! It ain't illegal yet!
George Clinton
How is this different from any other non-standard analysis approach?
That is all.
Infinity isn't a real number. Ergo, it cannot be the limit of a sequence, as the definition of a limit include the priviso that it is a real number.
You can only perform the substitution lim x->a f(x) = f(a) when f is continuous at a. f(x) = 1/x is (very trivially) not continous at a = 0.
Damnit, why is this sort of thing spilling over from sci.math now?
After all, I am strangely colored.
1. Slashdot should come up with a new section 'jokes'.
2. All editors post there.
3. Let the mod system also turn some readers into editors for a short while.
... where you can actually determine meaningful values for 0/0 in specific cases via calculus?e
I.e., it may well be that 0/0=a where a has a definite value? After all, any derivative is dy/dx=0/0.
That means to me that 0/0 is *really* undefined - may be this or that, depending on the circumstances; more information is needed, and assigning a specific symbol to it doesn't make much sense in the general case.
http://en.wikipedia.org/wiki/L'H%C3%B4pital's_rul
thegodmovie.com - watch it
... and dividing by zero while on the nullity line lets you go directly to World 9 with only two Warp Whistles!
This fantastic new math is also helpful in solving this intractable problem: http://mcraefamily.com/MathHelp/JokeProofFactoring .htm
How cool is that?
Seriously, it's hard to take someone like this seriously when he uses ignorant scare tactics such as his autopilot example. Either he's performing self aggrandizing hand waving, or he really is completely ignorant about the real world. Trust me - we do account for division by zero in autopilot systems. And - believe it or not - not only does the computer not "stop working" but we actually get a result back. It's called NaN. Furthermore, not only are our systems built with robust libraries that allow us to carry on (no pun intended) we also write downstream code to mitigate propagation of these types of errors. [see Celarier, Sando for a good example of this].
Trust me. This is an inactive account. Regardless of what the
The first paper he describes as:
The second paper he says:
He didn't solve the division-by-zero problem at all, he just hid it under a new definition; "nullity".
It's like saying.. what's beyond the end of the universe? Nobody knows.
Oh, wait, I do! It's "schmullity".
Yup, now we know what's beyond the universe's borders. No need to investigate any further.
From "Cugel the Clever" by Jack Vance:
"Here you see the pattern from which my great work is derived. It expresses the symbolic significance of NULLITY to which TOTALITY must necessarily attach itself, by Kratinjae's Second Law of Cryptorrhoid Affinities, with which you are possibly familiar."
Yes, I am the one with the legendary sig.
http://www.bookofparagon.com/News/News_00012.htm It's way too late for me to read these right now. Anybody know how this might be related to Conway's surreal numbers?
like the square root of -1, i
ugh...
Imaginary numbers are a perfectly valid construct, but yes, it's a bad name. Once you start dealing with electrical engineering, imaginary/complex numbers become very useful.
The best way to think of them is a number system perpendicular to the one based on 'real' numbers. This allows you to simplify the maths (or even make possible maths that wasn't possible before) when dealing with things like AC waves and phases. Engineers do similar tricks where they substitute a symbol in for a specific function.
It's sort of the mathematical version of using arrays, or variables, it's simply a way of representing 'the real world' in a simpler, more manageable way.
Remember kids, it's all fun and games until someone commits wholesale galactic genocide.
Imaginary numbers are useful when dealing with entities that have multiple quantitative attributes eg. electrical components that have both capacitance and inductance.
-1 (natural, linear numbering) is really (-1, 0) or (-1 + 0i).
Imaginary Numbers, changing the rules so that things work the way you want them to. Why is this (AFAIK) the only field to do this? How often do you hear a Physicist say "...
In as much as I love physics, I've always referred to it as a perversion of math. Any discipline in which you can divide away infinities in order to solve an intractable problem is definitely "changing the rules so that things work the way you want them to".
And before the physicists jump all over my case, I understand why this happens. And I also realize that you understand the change and work to account for it and justify it. But still - it is pretty funny when you look at it from a mathematical standpoint...
Trust me. This is an inactive account. Regardless of what the
Shouldn't X/0=X ?
You start with X, which is a real number, but since there's nothing to divide it by, it just goes *poof* ?
I think 0&1 should become the same number in division.
X/1 === X/0
Zero effectively nullifies the Operation ever happening.
Is that what this guy is trying to say ? I don't have RealPlayer.
Wanna fight ? Bend over, stick your head up your ass, and fight for air.
ALL Mathematics is COMPLETELY synthetic. That's the whole point -- that's the power of mathematics. You can define any set of rules, any set of axioms, any set of symbols, and start deducing. If the tools you need don't exist, you make them up. Nothing is more valuable in mathematics than a nice, clean, clear definition that increases the expressivity of math. Since math has no independent existence anyway, you can get away with pretty much anything so long as your new system has useful properties. Mathematicians with the guts to make things up as they go along end up with their names in textbooks and attached to great theorems, assuming what they made is conceptually useful (whether nullity is conceptually useful remains to be seen; a written description of the definitions would be nice).
Mathematicians that only do calculations that we already know about and are comfortable with? They're called accountants, and they have no friends. Seriously though -- since when did making up new ideas become a bad thing? I was under the (apparently mistaken) view that creativity was a praiseworthy trait.
Anyone who comes up with this crap should have his PhD revoked. Seriously.
All he does is call 0/0 nullity. And he states the obvious, 0^0 = 0/0. We all knew that, it is not a problem which has not been solved for hundreds of years. And he gives us a few howlers.
He defines infinity as 1/0. He defines -infinity as -1/0.
A sensible explanation of 0/0.
First, what is 0/1? If you travel 0 miles in 1 hour, what is your speed? 0/1 miles per hour (mph). 0 mph. You must have 0 speed to remain where you are after 1 hour.
Second, what is 1/0? If you travel 1 mile in 0 hours, what is your speed? 1/0 mph. Infinite mph. You must be REAL FAST, infinitely fast, to travel 1 mile in no time at all!
Last, what is 0/0? If you travel 0 miles in 0 hours, what is your speed? 0/0 mph. If you do 0 miles in 0 time, does that tell you anything about your speed? NO. You can be doing 1 mph. You can be doing 2 mph. You can be doing 0 mph. So 0/0 can be any number.
So this doctor's nullity should not be a point off the number line, it should span the whole number line. Revoke his PhD!
Again though, thank you for that quick n dirty explanation of Imaginary Numbers, I'm always eager to learn new stuffs. ^_^
How did this type of crank bullshit get on the BBC ? What's next, an article on the timecube ?!
In Soviet America the banks rob you!
I hear that Dr. James Anderson doesn't like to lose...
It must have been something you assimilated. . . .
I knew this good ol' 486 was right !
--
Intel errarum est
Submitter couldn't be bothered to do the research, but there is a paper written by this guy about the concept.
"Elmo knows where you live!" - The Simpsons
Poor little kids...
Seriously though this is the sort of thing that you don't want to sneeze at, it can sound both inane and brilliant. Anderson is not such a crackpot, I found a presentation of his on optical computing and an introduction to its underlying theory called perspex algebra ( "Representing geometrical knowledge."). He seems to be a geometer stating his perspective in the first line of that presentation: "Aims: To unify projective geometry and the Turing machine".
He's a geek hero! Who knows if his nullity will end up just NaN with a British twang or the next best thing to sliced bread and i?
I was unable to hear the realaudio casts but from Book of Paragon, The Perspex Machine (Anderson mentions transreal arithmetic) and Exact Numerical Computation of the Rational General Linear Transformations (a mathematical treatise with applications to computer vision and robotics) just glancing I'd have to say the guy seems to be a real mathematician, geek and philosopher-king. I don't know if he's up there with Newton but he at least deserves an honorable mention for his wonderfully witty (and to me as yet inscrutable) naming of the Walnut Cake Theorem (see page 10 of Perspex.pdf). It seems that he was motivated to create nullity in order to make reliable advanced computers that would not barf when asked questions about the universe, and to him "Not-a-Number" is vomit. I'd say read some of his stuff before assigning him to the 9th Hell. Would like to hear what any mathematicians or other people with brain cells over the age of 12 have to think about it. It's okay if he reinvented something but it appears he is trying to make a machine that can handle infinities and other tough numerical concepts with ease, and that's worth something. Oh, that and his quantum computer looks neat.
Every calculus student knows the answer to such questions as "what is the limit of 1/x as x approaches 0 from the right" (positive infinity) and "what is the limit of 1/x as x approaches 0 from the left" (negative infinity). And more usefully, derivatives are defined as "the limit of (f(x+h)-f(x))/h as h approaches 0 from the right". Integrals are defined through limits as well. So properly phrased (through limits) questions like this are the very foundation of calculus, and well-understood.
But "1/0" alone? What does that even mean? There's no answer. It's a stupid question, too oversimplified to distinguish between the possible answers. 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, saying that computers cannot divide by zero shows a ridiculous lack of common sense. They can do anything we design them to do. Many computer number systems (notably including IEEE 754) have 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 serious logic error. Imagine that airplane needs to calculate the proper elevator trim. Oh, great, the answer is nullity. What does that mean? How should it move the elevators? Giving this failure condition a new name doesn't change the fact that the airplane's still going to drop out of the sky.
As anyone who has done any calculus has learned, when dealing with operations over the real number field, 0 is a special number, in much the same vein as infinity.
... ...
o ofs/first1eq2.html )
In fact I remember having to solve this problem in my calculus lessons
What is sin(x)/x when x = 0? Now sin(0) = 0, so surely the answer to this should be Nullity?
If you try it on your calculator with x very small (but not quite zero) you'll see that the answer is 1.
Here is a proof
sin(x) = x - x**3/3! + x**5/5! - x**7/7! +
=> sin(x)/x = 1 - x**2/3! + x**4/5! - x**6/6! +
=> when x = 0, all terms except the first are 0, therefore
=> sin(x)/x = 0/0 = 1
I'm not sure it is really helpful having a symbol for 0/0. Might as well just call it x - the professors demonstration of what 0**0 would have worked just as well!
According to the professor
0**0 = 0**(1-1) = 0**1 * 0**-1 = (0/1)**1 * (0/1)**-1 = (0/1) * (1/0) = 0/0 = Nullity...
How about this version? Why did this get a different answer?
0**0 = 0**(1-1) = 0**1 * 0**-1 = (0/x)**1 * (0/x)**-1 = (0/x) * (x/0) = x/x = 1
If you start assuming that you can divide by 0 then you can prove anything (from http://www.math.toronto.edu/mathnet/plain/falsePr
a = b
=> a**2 = ab
=> a**2 + a**2 = a**2 + ab
=> 2*a**2 = a**2 + a*b
=> 2*a**2 - 2*a*b = a**2 + a*b - 2*a*b
=> 2*a**2 - 2*a*b = a**2 - a*b
=> 2*(a**2 - a*b) = 1*(a*2 - a*b)
=> 2 = 1
The last step is fallacious (a**2 - a*b) is 0
Every man for himself, all in favour say "I"
THEY MUST BE RELATED!!
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Anderson has a website with his theory explained in a series of PDFs. My take is that first he has to show that his idea is internally consistent. But there are uncountable (literally...) numbers of consistent, but useless theories. I don't see how it can have any practical significance -- just asserting 1/0 = nullity doesn't solve any problems that I can see. Certainly I don't see how it's relevant to computing, that can't handle real numbers like pi (without approximation), let alone infinity which does have a long established mathematical pedigree and use in analysis.
Actually, Mr. L'Hopital pretty much bought his theorem. Rather, Mr. Bernoulli would be the one saying something.
Watch the video this guy starts off defining -inf = -1/0 and +inf = 1/0. Yet basic elementary school math tells us that 0=-0 hence we get that -inf=+inf.
Now if you just want to set -inf and +inf equal to each other you get a reasonable mathematical structure. It isn't quite what we want from the real numbers since it fails to be a field but it's a lot like what you use in projective geometry.
All this aside what this guy says is just really damn stupid. First of all he is no longer working within the axioms of the real numbers so he didn't 'solve' any problem about 0^0. Second of all he seems to lack any understanding of what the content is of asserting what 0^0 would be. It sure as hell isn't just doing some computation. It would have to work consistently with all our other expectations about how exponentials and limits work and you just can't define something that works consistently like this.
I mean jesus christ do people like this not realize that there is an entire profession who does math and has dealt with this sort of thing a LONG time ago.
If you liked this thought maybe you would find my blog nice too:
Thanks to the groundbreaking work, I have to buy the second edition of this book.o urceid=39391960&isbn=0743258207
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Thank you very much!
0/0 is special, explained:
Think of a division as the reverse of multiplication:
6 / 2 = 3, which means 3 * 2 = 6
With a division by 0, this does not hold:
6 / 0 = x, there is no possible x for which x * 0 = 6
X can be no real number
However, 0/0 is different:
0 / 0 = x, but no matter what you fill in for x, x * 0 = 0
X can be any real or imaginary number, 0 * x is always 0
This is why A / 0 has no solution, unless A = 0, then A / 0 does have a solution, an infinite number of solutions in fact: all numbers are a correct solution.
This professor didn't invent it by the way. He just seems to be the first to bother explaining it to school children.
The way you have it matches with the axioms in the original source: http://www.bookofparagon.com/Mathematics/PerspexMa chineVIII.pdf
James Anderson suggests nullity "lies off the number line." Lovely, but has he considered nullity's place on the complex plane? Does nullity exist outside that as well, or does it represent a sort of infinity or zero or negative infinity of the z-axis? What is nullity divided by nullity, or better yet, nullity to the power of nullity? The idea should see some cultivation before being taught as it is to ingenuous young schoolchildren.
... you say that like it's a bad thing. What's wrong with restructuring math? As you say, it's been done many times, and some of those times it has been restructured to positive effect. Designing a new system is great, if it's a good system. Furthermore (and this is my favourite line, since it makes no sense at all) "inventing his own false reality"?! Mathematics is not reality in any sense, false or otherwise. Mathematics is just dumb little symbols on paper that can be replaced by other dumb little symbols according to ridiculous rules. This is no different than adding i or omega or negatives or the aleph numbers or defining hyperbolic geometries or any other new mathematical idea. It could be much less useful than those ideas (and it probably is, since it depends on 1/0 being infinity and -1/0 being negative infinity, which isn't very practical), but it's no more true or false than they are since mathematics is totally imaginary to begin with.
These four really nice guys on horses arrived and asked me directions a couple of minutes after. Invited them in for a bit of tea and cake, really nice fellows, terrible dermatitis, gave them a card for my dermatologist but I think once you get past the point of seeing bone there's not much you can do.
They talked a lot about scythes, not very interesting conversation.
Task Mangler
Ummm, I think you got usernames confused. You're ET Fleshy. I'm wasted.
he rediscovered the axiom!
A Good Troll is better than a Bad Human.
IEEE 754 floating point numbers have +/- infinity built in, and N / 0 = infinity. This is hardly a new discovery.
So, why do computers still complain when we divide by zero, instead of just returning infinity? Because we want them to! Dividing by zero almost always represents a logic error in your program, or invalid input from a user, and it's far better to produce a meaningful error in those cases than to continue happily along with nonsense data.
It's just past 2AM and it's already slow news day?
Slashdot, how about waiting at least until 5PM before posting fluff pieces to fill up the page?
Only Chuck Norris can divide by zero.
Chuck Norris just looks at zero, and it divides itself.
Soylent Green is peoplicious!
Osho
From the mathematic point of view, infinity is not a number. infinity is a limit.
You can't say "1/0=infinity" . 1/0 is undefined.
You can study f(x)=1/x and see that when x -> 0 and x > 0 then f(x) -> infinity
or that, when x -> 0 and x -infinity
From the computer science point of view, it's useful to have a special representation for undefined mathematics results. So, in some (recent) languages, you can find NaN, +infinity and -infinity. But all of them are not numbers, they are error results of arithmetic operation.
A complex number has a real and an imaginary component.
Either or both components may be zero.
If only the imaginary compnent is zero, then you have a real number.
If only the real component is zero, then you have an imaginary number.
If both components are zero, then you enter an alternate universe where Darth Vader isn't Luke's father or something.
Either that, or you just have zero.
Those who sacrifice security to condemn liberty deserve to repeat history or something. - Benjamin Santayana
Zero comes up with way to divide professors.
Not to mention quaternions, which can make computation of complicated 3D rotations trivial. I won't talk about octonions, as I really don't know of any significant uses of octonions. ;-)
http://links.jstor.org/sici?sici=0962-8436(1997082 9)352%3A1358%3C1129%3ARGK%3E2.0.CO%3B2-0 (at least originally by Mr. Anderson).
Wow. Looking over the guy's axioms, as soon as you introduce "nullity" the result of all of your computations is nullity:
- the sum of anything and nullity is nullity (his axiom A4)
- the product of nullity and anything is nullity (his axiom A15)
- the reprical of nullity is nullity (his axiom A22)
So, his arithmetic is normal arithmetic, but as soon as you hit nullity anywhere, it's a black hole you can never get out of. All he's essentially done is take the "error state" and add it into the system as an object. You still can't compute anything you couldn't compute before. So yes, he has truly discovered NaN.
Well, as you said math is definitely NOT your strong suit. The problem with "Imaginary Numbers" is that the name is unfortunate. The word "imaginary" conveys that they are something abstract and not planted in the real world, the opposite is actually the Truth. Most of the 20th century science and engineering has something to do with "complex" numbers (I think is better if you use this term instead). Almost everything that "spins" in some way is related with complex numbers, waves for example, you cannot deny that a lot of things in our modern life if governed by waves i.e. radio waves, micro waves, infrared light, etc. Predictions and design via quantum mechanics are possible due to complex numbers!!! Granted, these numbers were originally "discovered" (rather than invented) and they were no more that a mathematical curiosity, but later Quantum Mechanics made heavy use of them and gave place to modern optical and electronic devices ... so much for something that is "imaginary".
Regarding this Dr. Anderson, it seems that his "findings" are a complete screwed up.
Comment removed based on user account deletion
It's nothing different that adding an "error" value to a data type. Remember the school, when defining the "stack" abstract data type, you can set "pop(empty)" to be the "error" stack (and of course, "whatever(error) = error")
I think you'll find that relational algebra does NOT permit NULLs -- if you want a column (field) which can be "undefined" then you build that into the data type of your field instead of just arbitrarily declaring that any field may have the value "undefined". The principle that all fields have some value (even if it is semantically "undefined") is in fact what makes relational algebra so elegant.
James Anderson: The numbers all divide by zero. Look, right across the board, zero, zero, zero and...
Marty DiBergi: Oh, I see. And most calculators only go down to 1?
James Anderson: Exactly.
Marty DiBergi: Does that mean it's one smaller? Is it any smaller?
James Anderson: Well, it's one smaller, isn't it? It's not one. You see, most blokes, you know, will be dividing by one. You're on one here, all the way down, all the way down, all the way down, you're on one on your calculator. Where can you go from there? Where?
Marty DiBergi: I don't know.
James Anderson: Nowhere. Exactly. What we do is, if we need that extra push over the cliff, you know what we do?
Marty DiBergi: Divide by zero?
James Anderson: Zero. Exactly. One smaller.
Marty DiBergi: Why don't you just make one smaller and make one be the smallest number and make that a little smaller?
James Anderson: [pause, blank look and snapping chewing gum] These divide by zero.
I'm not claiming to be a doctorate in anything, but this is the stupidest thing I've ever seen. I've used i in equations (sqrt -1), which also exists on another number line. But it wasn't because I just made up a loose logical term. Show me what I do with this "nullity" after I've gotten it returned, and am spinning headlong into the runway. "Sure your heart stopped Stan, but at least we got an unicode character in the debug!"
I haven't RTFA, but I find it already perfectly usefull - if not a bit simple. If x/0=x nullity (it has to be, otherwise there'd be no way to invert the equation), then x nullity * 0 = x. So nullity is, in fact, the cancellation of a multiplication by zero (nullity * 0 = 1). Perfectly usefull as a function if you don't know what you're multiplying with, but _don't_ want to end up with zero if it's zero.
Religion is what happens when nature strikes and groupthink goes wrong.
And guess what you'll get when you divide a number by zero and then multiply it by three?
This was a question posed in a book I read a while ago, by some reknown mathematician...for all his accomplishments, he couldn't help but wonder...was any of it really helping to describe the universe better and broadening our knowledge of it (thus, a discovery), or was more of it simply a figment of his stretched imagination?
So Nullity may now 'officially' mean n/0 but what does it mean really? Is it just another term for, say, infinity or undefined?
I thought he lived circa 500 BC, which would make the problem at least 2500 years old, not 1200, if he were working on it.
Well, if we are talking about the real numbers, then we know that they conform a field. Now, if we add another element and a property such as infinity = 1/0, while trying to preserve the already existing structure, then the following problem takes place:
1/0 means that 1 is being divided by zero, but if a number is divided by zero it means it is being multiplied by the (multiplicative) inverse of zero. But, because we are trying to keep the real numbers a field, 0*(0^-1) = 1. Thus, if we multiply this time both sides by, say, 2, we have 1*2 = 2 = 2*0*(0^-1)= 0*(0^-1) = 1. Then if X E R, then X = 1, including the zero. We then have that R = {1} (In this case the 1 is the multiplication identity and the additive identity).
So he must be breaking some convention at some place if he claims that he can divide by zero without severely affecting the real numbers as a set.
... but my RealPlayer divided by zero and crashed.
Claiming to be pedantic on Slashdot is asking for trouble
That's just stupid. RTFA looks more like joke than any kind of serious science.
You cannot divide by zero by definition. It's the property. Read on. And in real life rarely need arises. (Try to divide $1Mln amongst 0 people. Good luck.)
One can also devise a number space where division by 0 would give some result. That's not a problem as it is. Per se, it's the problem of computer created to solve physical tasks and taken standard math. In fact, programmers can always disable the nasty division by zero exception. Not that it would really help: result is still undefined.
Worth to mention, that problems caused by division by zero are just superficial and incorrect. Any reliable system which requires division operation are normally do not use division at all: in many cases it's trivially replaceable with multiplication and rest of the cases it is replaced non trivially by modifying algorithms.
Most of such work is already done. In university, all numerical algorithms we have studied never relied on division by variable. More than decade into software development and I cannot really recall a single time when I have had a possibility of division by zero: zero in many situations isn't valid input anyway.
All hope abandon ye who enter here.
This has to be a hoax of some kind. I can't believe they let people this dumb teach math.
The same sort of manipulation this guy does can easily be applied to show that 0 = nullity.
0=0^1=0^-1 * 0^2 = 1/0 * 0*0 = 1/0 * 0 = 1/0 * 0/1 = 0/0 = nullity.
How can someone who is supposedly trained and licensed do this to kids.
If you liked this thought maybe you would find my blog nice too:
What's so amusing about that? Nah, what's amusing is the fact that exactly zero (0) slashdot nerds know that this is in fact the correct answer, and that the professor is wrong.
The answer to a / 0 is defined as the limit for a / x when x approaches 0. Some examples:
23 / 0 = lim x->0 (23 / x) = inf
-5 / 0 = lim x->0 (-5 / x) = -inf
0 / 0 = lim x->0 (0 / x) = 0
Simple as that.
Disclaimer: I haven't read the fine article, perhaps the professor meant something else.
Not so -- a lot of the time, physics actually drives the development in mathematics (take calculus, for example).
We define three new quantities: An enormous pile of crap, a negative pile of crap, and a pile of crap of unknown size.
0/0 is a pile of crap of unknown size.
a/0 is an enormous pile of crap if a > 0, and a negative pile of crap if a 0.
Any operation involving a pile of crap of unknown size produces a pile of crap of unknown size.
Adding anything to an enormous pile of crap gives an enormous pile of crap; adding anything to a negative pile of crap gives a negative pile of crap, the only exception is that adding an enormous pile of crap and a negative pile of crap gives a pile of crap of unknown size.
Piles of crap of unknown size cannot be compared to anything.
Multiplying any pile of crap by zero gives a pile of crap of unknown size.
Do I need to continue?
Basically, he has done something in a way quite similar to the IEEE 754 Standard, by defining Infinities and NaNs. However, he didn't define positive and negative zeroes, which makes the whole thing much less useful. And the rules for arithmetic are full of exception after exception, except that he claims the exceptions are part of the rules and therefore not exceptions.
Did I mention a pile of crap of unknown size?
The nullity theorem depends on Infinity being defined as a number, Infinity is not a number it just like the + sign is not a number +/+ != 1 because + is not a number. Infinity is simply a concept that means "too big to be defined"
..that universe might collapse because of this.
Is that if I tried this kind of cheating at university, I would have been thrown out of the classroom with a boot-shaped mark on my rear end.
"Discovering" this miraculous new number sounds like winning at the Kobayashi Maru test - by changing the rules of the test itself. Thus, cheating.
Anyone want to attempt a practical application of this so called *invention*?
I still fail to see how this helps people with pacemakers and computer related problems. Firstly any decent computer programmer making high integrity systems must care for situations where the divisor could be zero. Secondly there is no magical solution just by inventing a new concept. If your computer program should - even after your persistent effort - in an unforseen circumstance throw an divide-by-zero exception then just handle the exception and carry on.
I will never forget when I was about 8 years old going up to the adding machine in my grandfather's home office. It was about twice the size of a toaster and made of that old typewriter metal. It looked like it weighed as much as a car and had probably cost as much new. Just to see what would happen I entered '0', '/' and '0'. Without hesitation it began producing line after line of '0', '0', '0' on the paper tape accompanied by a cacaphony of mechanical gears. It became apparent to me in a split second that it had no intention of stopping. Ever. It had come alive and was angry.
I yanked the plug from the wall socket and ran from the room in terror.
It depends on how you get there.
A=X B=1/x
lim as X->infinity
a-> infinity
B-> zero
so for A*B, yes it does equal 1, which when you reduce it is obvious since X*1/x =1
And no, I'm not joking, This is really how you are supposed to think about it, as they explain when they teach limits in calculus.
Wow. A proof of a tautology. That Fields Medal is coming right your way Dr. James Anderson!
Having scanned the papers, I think I understand the underlying motivation for his creation: he doesn't intend to replace real numbers, where infinity is a limit, but to improve on IEEE floats, where + and - are actual numbers and you indeed have 1.0f / 0.0f == 1.#INF. The problem is that good ol' NaN is not mathematically consistent. A lot of library functions will spit out NaNs when used outside their domains, but NaN's properties do not match the conditions that bring it into play. He has a dislike for the fact that NaN != NaN, which is useful to us to detect an error condition, but has no mathematical justification beyond conventions set out in the IEEE 754 standard. Of course, presenting division by zero as an unsolvable problem for computer scientists is unfortunate hyperbole, and teaching students to work with his structure in regular coursework is misguided: it belongs in an abstract algebra course. But conceptually, while his idea probably won't cause revolution in computer engineering, it isn't complete nonsense either.
While a math person would strangle another math person for saying something like that, I was a math/physics major, so I'll tell you that at least in the sciences, you're dead on. It so happens that a lot of really messy operations (particularly trig ones like sines and cosines) over the real numbers look really clean once you realize they are just the real/imaginary parts of simple imaginary functions.
...), which is an infinite sum that only converges to a finite value if the real part of s is greater than 1 (for example, if it's zero, we have zeta(0) = 1+1+1+1+...). We can define its analytic continuation for other values, though, and prove interesting and unintuitive formulae like 1+2+3+4+5+... = -1/12 (which is, amazingly enough, actually somewhat relevant in physics when you look at the Casimir effect or string theory - it's the reason that in bosonic string theory you need 26 dimensions for quantum consistency, as in 2(left/right moving waves)*12(magic number from the zeta formula which counts energies of each mode) = 24, the number of degrees of freedom of a 2 dimensional string world-sheet).
Another way to think of it is that complex numbers are just a really special way of dealing with 2-dimensional geometry, where scaling and rotation are represented by complex multiplication. i corresponds to a 90 degree rotation, which is why i^2 = -1 (i.e. a 180 degree rotation). It's also why you can arbitrarily choose whether i is a clockwise or anticlockwise rotation as long as it's a consistent choice: two -90 degree rotations are equivalent to two positive ones (um...I hate to even bring it up, but that's actually not true in physics, where we have spinors - imagine a book attached to a ribbon which is attached to a table, and imagine turning the book 360 degrees; the ribbon is now twisted, and without further rotation it can't be untwisted, but if you rotate it another 360 degrees, you can undo the twisting without moving the book, by sort of pulling the loop of ribbon over the book - try it out if you're confused. That's the essence of a spinor, that a single full rotation leaves it in the "opposite" state, and that it leaves you confused).
Now I'll take off the science hat and put on the math one...the reason mathematicians love complex numbers is that if you have a function f(z) that is a function of the complex number z = x + iy (where x and y are both real), but not a function of x or y alone (i.e. f(z) = z+z^2+e^iz qualifies, f(z,x,y) = x - y + z does not), there are many subtle and powerful qualities that that function must possess. The one that comes up a lot is that you can do a Taylor expansion of the function and it "works" within a well defined range of values; another nice thing is that integration of the function along closed paths is all but trivial (it's always zero unless it encloses a "pole," i.e. a place where the function blows up in a certain way). As it turns out you can also take a function that you've defined along a single line (or piece of a line) and use its Taylor expansion to extend it to the whole complex plane. This is especially nice for functions like the Riemann zeta function (zeta(s) = 1/1^s + 1/2^s + 1/3^s +
So in summary, complex numbers are very important because they give us so many results that we could not even approach any other way (I haven't even mentioned the more subtle ones, esp. having to do with prime numbers!). To the contrary, the stuff that this professor is pushing seems entirely useless, more of an attempt to push a new term rather than a new concept. Mathematicians have understood infinity and what you can and can't say or do with it for a long time; anything you could even try to explain to a bunch of schoolchildren is either wrong, old news, or irrelevant.
Don't forget about Sedenions, which is likely the most beatyful of the hypercomplex numbers (and probably the least useful one XD).
Carbon based humanoid in training.
Euler's Identity - 'nuff said.
I used to see e ^ i theta as the essential conjoining point of geometry (i.e angles and trignometry) into the imaginary plane (which is really another co-ordinate system). Some inner beauty of the system where all math is connected, rather than divided into chapters in a textbook.
But cheap indian labour has little use for abstract math :(
Quidquid latine dictum sit, altum videtur
What he did was simply to name the animal, so you can handle it ... with care!
...
100/0 = inf
10/0 = inf
does not mean 100 == 10
infinity / (infinity - 1) != 1
true, but then again
infinity / infinity != 1
maybe he also should have invented infinity / infinity = infinility?
or
since infinity = 1/0 it means
infinity / infinity = (1/0) / (1/0) = 0/0 = nullity?
In other words, nullity is just your "crazy elite math speek" for NaN.
Tristan.
Its a maths discussion. The same rules don't apply. Who modded parent to 5 FFS??
Indeed, he hasn't invented anything new ... every computer has always dealt with the matter the way he purposes: 1/+0 = inf, 1/-0 = -inf, 0/0 = NaN. Only he named NaN nullity.
The whole nullity thing is ridiculous... so he comes up with an approach for solving 0^0 and then comes up with 0/0, then decides he's fucking brilliant by calling it nullity, when essentially he's just shown yet again that the whole problem is undefined.
In reality, 0^0 depends on how you GET THERE. Did you get there by limit X->0 of X^0? Well then it's obviously one.
Did you get there by limit of X->0 of 0^X? Then it's obviously zero.
And if you Apply the same logic to his "proof" you get the same results.
What a giant load, and the sad part is some moron is going to give him a grant for this.
Oh give me a break.
Here's two equations:
x * 0 = 6
z * z = -1
You'd actually argue that the first equation, which actually has a simple answer, violates basic mathematics while the second one, which cannot possibly have a real answer is valid because mathematicians made up an imaginary number?
The answer to the first equation is 6/0 (or 6*nullity if you wish to write it that way.. nullity being 1/0). Here's my proof:
6/0 * 0 = 6;
0 cancels out, and you get 6=6. You'd complain that you can't divide by zero, but I'd claim that if I had written a/b * b = c you wouldn't think twice about canceling b out. It doesn't matter if b = 0 or not.
Therefore x/0 does exist, it is a valid construct and, exactly like imaginary numbers, it's really only useful if it's used in an equation that cancels it out.
You thought you couldn't calculate log(-1)?
Well, you were wrong! Today you can also be one of the select few who are allowed to use my number: Qumph.
For only a small amount you can get a license to do really neat and strange mathematics.
From his board:
1/0 = infinity
0/0 = nullity
(1/0) * (0/1) = infinity * 0 = nullity
So nullity is a whole lot of nothing.
Got it.
Any non-zero number divided by zero = infinity .00001/0=infinity
IE: 100/0=infinity same as
Any zero divided by a non-zero number = zero
IE: 0/100=0 same as 0/.00001=0
Any number divided by itself=1 .00001/.00001=1
IE: 100/100=1 same as
It seems not totally unreasonable to me for the two first rules above (100/0=infinity and 0/100=0) to cancel each other out in the case of 0/0.
However, a simple progression the third rule I listed above does seem to remain true as both numbers approach zero at the same rate (ie remain equal). .00001/.00001=1 same as (1x10^-1000)/(1x10^-1000)=1
IE: 10000/10000=1 same as
Am I oversimplifying things? Because to my mind, 0/0 should equal 1.
Hands down the dumbest fucking thing I've read all week... and I read the general help forums for ubuntu.... so yea... it's that bad.
0/0 = shut your god damn mouth
You can't take the sky from me.
Quaternions are basicly used as a trick in Computer Animation , because you can "misuse" them inorder to describe a rotation as vectors. And the good part is that you can use all the Quaternion math to manipulate them ( it's fast). Also they have no problems when the first rotation is exactly around 90( with Euler Angles it kills of 1 dimension). But they aren't really used because it is by far simpler for the animator to use Euler Angles ( turn 40 at the X , 50 at the Y and 60 at the Z) .
-- TRUST ME! I KNOW WHAT I'M DOING!
If he can make up numbers, then I cam make up words,
this whole thing is utterly stuipfluous.
6/0 * 0 = 6
and 0 * 7 = 0 (7 is arbitrary, could be any real number)
6/0 * (0 * 7)=6
(6/0 * 0) * 7=6 (6/0 = 6, like you said)
6 * 7 = 6
42 = 6
Hmmmmm, something seems to have gone horribly wrong here. Care to enlighten us?
Ignorance is not linguistic drift.
I can't understand it. So where is it exactly? Does it overturn the entire N-dimensional world?
My fingers just got all tied into knots!
This silly number is completely uninteresting compared to the other amazing work that can be found on some website someone linked to. Like the Perspex Machine!
"The compiler generally lays out perspexes along a straight, spacetime line that changes only in time, t. However, the compiler implements C conditionals by jumping additionally in the spatial dimensions x, y, or z. C loops exploit a backward jump in time to iterate the loop. This exposes an infelicity in the specification of the perspex machine. Whilst the perspex machine can support such arbitrary temporal jumps it cannot copy them directly. It must use additional geometrical transformations and the access column to prevent an arbitrary temporal jump component being reduced to a normalised jump component of 0, 1, nullity, or infinity. This is remedied by the introduction of the universal perspex machine."
He is seeming to claim that the reciprocal is some kind of superset of the multiplicative inverse, having that it has two distinct multiplicative zeros (0 and Phi) that both have reciprocals. Now "numbers" as we use then to do real sums, and not just talk shit, have certain useful properties, such as being in a ring, wherein we have the result that if there are two zeros they must be distinct:
a x 0=a
Phi x a=Phi
So 0 + Phi = 0 and 0 x Phi = Phi, so 0=Phi... but it isn't so we don't have a ring, and we don't have anything that looks much like numbers.
I fail to see how introducing brokenness to numbers makes them more useful.
If this is real, who will solve the problem of divide by nullity? Sounds like he's just adding another problem to solve the first one.
That's why he's defined a new arithmetic - he calls it transreal - where division by zero is defined. The PDFs on his website clearly explain what he's done.
It isn't rubbish. In second year high school mathematics they had us "invent" our own arithmetic. We could define whatever operations we like (eg, a funny symbol that would multiple the left hand value by 2 and add it to the inverse of the right hand value) and then we had to prove whether the operation was commutative, distributive, etc. This guy has done the same thing but with a new "number" he calls nullity. He has defined what happens when you add a real to nullity, when you multiply a real by nullity, when you divide nullity by nullity, etc. It's an internally consistent number system.
It's interesting for grade schoolers because it gets them thinking about number theory. Instead of thinking "you can't divide by zero" they instead think "oh, well that's just a law for the real numbers, but I'm not constrained by real numbers, I can invent a number system where division by zero is allowed". That is far more insightful and creative than "you can't divide by zero". A child who grasps that concept has the potential to become a great mathematician. A child who merely parrots "you can't divide by zero" will become a bus driver or a computer programmer :-P
It's hard to explain abstract concepts such as number theory. Congratulations to him for making it look like fun.
AHH! Boas' "Mathematical Methods In The Physical Sciences."
Its a good book. However one of my fav tidbit gleamed from its pages is why Square roots have 2 numbers associated with it and that in actuality the Nth Root of a number has N seprate answers. N-2 imaginary if even and N-1 if odd. Pretty fun stuff.
For a Nth root of a number take 360 degrees of a circle and divide it by N to get a how many degrees between each of the answers for your problem in the complex plane. The hypotinous being the original number and given the fact that you have theta you can find the real and imaginary part of each answer. If you noticed for even Ns the degrees allways land on 180 and 360 refeering to the negative and positive root. So remeber when you take the 8th root of something be sure to check all 8 answers =D
Never could figure out why my girl liked my bitch tits, then I found out she was a lesbian.
(n/t)
I just solved the P=NP problem. The answer is peeequalsennpeeanswer - a special word I made up which represents a complete proof.
so nullity means goto end, stop computing?
Organization: alphabetical, sometimes numerical or messy
I can't vouch for the validity of "nullity" mathematically (associativity, distributivity, invertability etc) but I think people may be looking at this in the wrong way. That is, too practically. A computer would also throw an error (generally) if I try to take the square root of negative one. Of course, if you are using a math library that understands complex numbers the it will return i. i by itself is completely meaningless. What makes i powerful is some very abstract maths that has taken many years to come up with practical uses (See Euler, Fourier etc). For example, e^(i*pi) = -1 and things like fourier and laplace transorms. Who would have thought for example that knowing the complex/imaginary roots of a polynomial that does not cross the x axis could tell us the steady state error of a navigational control system?? It makes no sense at first. A lot of maths is not immediately clear in its application.
Its not just about saying I can't think of an immediate practical use for this number so I will bag it. It may take a hundred years before anyone comes up with a practical use for this. The missing link is a mathematical relationship netween nullify and the maths we already know - if there is one!
The real issue here is not the nonsense this guy has come up with (others have shown why this is not only useless, but actually causing trouble, mathematically).
The real issue is why BBC (and maybe other media) spread this nonsense. Will we read about somebody with a "Dr" in front of his name who has constructed a perpetuum mobile or squared the circle next time? Will, in a word, BBC make an article out of any nut who claims he has solved a long-standing problem without going through the trouble and checking with one or two experts first?
It's infinity. A concept we are all already familiar with.
Think about it.
I seriously hope this professor knows something about algebra.
He's just unioned the extended real numbers (reals with +/- infinity) with some new number "nullity" which amounts to the inverse of the additive identity (zero). At this point he is no longer working in a FIELD -- a well defined algebraic structure from which many of the properties of the reals come. He is messing around with some construct that is based on absolutely zero abstract algebra. His regular algebra tricks like "to multiply fractions we multipy the top by the top and the bottom by the bottom" don't apply in this system. Here's a simple consequence of his arithmatic:
[using the multiplicative axiom: nullity*a = nullity
additive axiom: nullity + a = nullity
and the arithmatic the professor used in his "proof"]
Let 'a' be an element in the construct:
a = 0 + a = (0^-1 * 0^2) + a = (1/0)*(0)^2 + a = (1/0)(0) + a = (1/0)(0/1) + a = (nullity) + a = nullity
Thus every real number a is nullity
So, if we follow the nullity axioms and use his arithmatic we reduce these trans-reals to the trivial group {0}.
The saddest part of the story is that the poor children in the video had to watch this jerk fumble around on the board to show his new definition (through an incorrect proof) a definition for 0^0. Then this guy has the audacity to claim he'd solved a "1200 year old problem" in a few lines on the board. It sickens me to see this man's "nullity theory" could be compared to the works of Newton or Pythagoras.
Hello,
devision by zero is possible for at least 100 years - in appropiate structures like the "Riemann Sphere". (http://en.wikipedia.org/wiki/Riemann_sphere)
Furthermore, if you construct a structure just by adding a value for z/0 - this won't solve anything.
- z/0 is somewhere around infinity - why not call it infinity?
- Riemann did a good thing by saying: Let -infinity be +infinity.
- Adding values like +/-infinity or this new shit to defined structes will screw up a lot of rules.
E.g. What is the additive inverse of this new - so called - number? Get it - there is none.
Thus folks, lets stick at the Riemann Sphere to solve division by zero trouble.
cu
Shouldn't 0 divided in x just result in smaller fractions of 0
Most of these objections can be dealt with by reading the actual paper. They do discuss NaN and how their formulation is different.
They are extending the reals with (at least) three extra quantities namely + (plus infinity), - (minus infinity) and ('phi'). The authors define the basic addition and ordering operations for all of these.
Pacemakers (I have been told) do not stop when they get an arithmetic exception anyway. The on-board computers are just for monitoring and recording; they do not drive the actual main circuitry. (This is NOT professional advice; make your own enquiries...)
Regards, Martin IT: http://methodsupport.com Personal: http://thereisnoend.org
So let me see if I have this right: if I have a mathematical problem I cant solve (and God knows, there are a lot of them) then the answer....in a flash of self-proclaimed brilliance.....is to simply make up a new number or number-like thing, and say "thats the answer...not that it really exists or I know what it is or that anyone can prove it"??
Shit, all those nearly failed maths tests I could have romped home, the missed potential PhD in mathematics I could have done.
I need to find someone to sue!
A then Ph.D at the University of Stockholm provided with a much better construction of division by zero, called wheels. http://www.math.su.se/~jesper/research/wheels/ Mathematical Structures in Computer Science 14(1):143-184, Cambridge University Press, 2004
Nulity is -infinity all the way through to +infinity. By my reconing the answer to any question involving a number as it's answer is now nulity.
The price of bread = nulity
my speed when driving = nulity, which may or not be in the legal limits of the road on which I am traveling, which is roughly nulity.
Okay. You got me. I am all for modern math in schools.
But. As a person being long into math and algebra, I find his claim plain "wrong". Especially as related to computers. You cannot make up problem to introduce solution. (A.K.A. solution in search of problem.) Probably that makes math easier to understand, but still he is in fact reinterpreting reality. I doubt it is good way to teach kids.
Bending reality so that it would solution: that's why mathematicians are so isolated from society. They have to deal with tasks set in weird realities - often "ideal" realities having no problems. Well, just like virtual reality of computers abused by people to get away from real world problems.
Kids need to be taught how to deal with real world problems: not how to come up with funny solutions and then stretch reality to fit the solution.
All hope abandon ye who enter here.
When one considers the absolute fact that mathematics is a MODEL OF REALITY and not reality then one has to understand that null or nullity is the answer. This really should not be weird to C++ types. They hit this creature all of the time as an error that requires a try/catch.
To understand this you need simply to start with a reaction. This is that famous widget thing from Accounting so don't get messed up here. Supposing you take 1 of something and react it against 1 of another. This is division of 1 by 1. Try reacting a Billion of something against 1 of it. Now that is always 1,000,000,000/1. A little factor here comes into play called vector. I know the math types out there who have died and become GOD will object but you always get this fraction because all reactions are many divided by the fewer. Its a natural law that seems to have been forgotten in math. Now try reacting 1/2 of something against a 100. This is a fiction. Because the smallest number of something you can ever have in the real world is 1. If you don't have 1 of it, you have none of it. Another model limitation that got forgotten in math. All natural math is integer math. Computer types should understand this! So lets try a reaction where we react a billion of something against none of it. This is 1,000,000,000/0. The model answers back with that natural law limitation that there is no reaction. NULL is the answer. There is no address to dump a non-reaction.
The reality is that this professor is right but I really wish he wouldn't try to invent a new term for it. Try the famous computer science C++ solution that has been around for years NULL! Its right! Its right for the very same reason it has been showing up for years in C++. Now this leads to a very serious reality. Those who have been hanging out in their Floating Point approximation world are going to have to realize that it is an Approximation --- Literally a close error but not the truth. I don't hate floating point math, but what we need to do is understand this.
There are profound conclusions this leads to. It limits reaction predictions in math. This eliminates -- (For those who don't understand -- I mean entirely wipes out) the Cosmological conclusions about the Speed of Light being a limit on velocity. It eliminates the illogical conclusions of the age of the Universe and sorry for those trucking the load for Special Relativity, but it clobbers them in the teeth and removes the entire calculation set that infers the Big Bang. Of course had you checked with the IEEE - cosmology section and their discussions you might have found out that the science had departed and gone somewhere else a long time ago. The electrical universe is but one of the things that arrives fully fledged if you accept NULL. (non reaction with nothing) Cosmology is but one science area that really gets hit in the face by NULL. There are a lot of others.
Never Politically Correct ~ I prefer the facts If you don't like what I say, get a life, or comment yourself.
(nil) = 0/0 = 1 * (0/0) = (1*0)/0 = inf * (0/0) = inf * (nil) and this yields: inf = (nil) / (nil) = 1
That's all folks!
If you postulate the existence of this non-number, thus you can calculate apples with peers... I hope they don't code it in good olde BBC basic. As everybody must know, (0/0) = 42...
Suppose...
x/0=y
x!=0
Which means...
x=y*0
x!=0
Which means...
x=0
x!=0
Which is never true, QED, so "x/0=y" does not generate a value for y when x is non-zero.
Suppose...
x/0=y
x=0
Which means...
x=y*0
x=0
Which means...
x=0
x=0
Which is always true, so "x/0=y" could generate a value for y when x is zero
The equations tell us nothing about what this value is, so I'd prefer it to be "0/0=unknown" rather than "0/0=infinity".
Reduce, reuse, cycle
I'm sure this story bear no relation to the fact that the University of Reading is (or was when I last looked) one of the few institutions in the UK to accept admissions to Comp Sci without a Maths A-Level.
My wife is a mathematician, and in a very pure area at that. Not that I understand any of it, but most of what she describes to me sounds totally useless. If she didn't have students to teach this to, I can't imagine what she'd do.
The only part that adds up is that she's that rarest of creatures, a totally hot female mathematician.
You are welcome on my lawn.
So tell me, what does 0 ÷ nullity equal?
That's incorrect!!!
You can derive that equality 0 * x = 0 only if your original equation 0/0 = x makes sense first.
In order for that equation to make sense, x has to be an actual specific number, not any number.
It wasn't meant as a mathematical proof, it was meant as a simple illustration why 0/0 is a special case of division by zero.
Anderson is somewhat of an avid writer.
On page 140 (type in page 154 in Acrobat Reader) in his book you can read a letter he has written to the future fleet of elite androids, powered by his super-Turing machine (which he calls a "perspex").
An excerpt:
Claiming to be pedantic on Slashdot is asking for trouble
Quaternions are great, but rarely used in practice anymore.
Since the discovery of vector methods, they've basically been superceded.
The Quaternion Group is a great one, though.
Its the DBZ bug!
I just had a breakthrough myself! I found the full value of Pi: . It's been right here the whole time! Who knew?
Great Intellect...
that E means 14 in hex?! It is absolutely obvious that E means 2.781...
When I was learning limits in math, I was told that x / 0 = infinity. I always thought that in computer languages, or computers in general, it was much more a matter of representing this in the computer than knowing the "value" of the equation.
Regardless of whether he works in the trans-reals or not, his "proof" of 0^0=nullity is wrong. It hinges on the fact that he can factor 0^0 as 0^(1 - 1). Here's a simple consequence of this:
Note first that 0 = 0^1 = 0^2
0^0 = 0^(1 - 1) = 0^(-1) * 0^(1) = 0^(-1) * 0^(2) = 0^(-1 + 2) = 0^1 = 0
Thus we get 0^0=0. But everyone and their dog knows that 0^0 is undefined for the usual definition of exponent. Great arithmatic "professor". It's really sad this got on the news. Even more sad is the fact that it made it to the front page of Slashdot.
Can a math-type comment for me?
I'm aware of the argument that multiplication and division are inverse, that so [any value]*0=0, thus 0/0=[any value], but that seems to be a byproduct of defining division in terms of multiplication. I'm also aware that it would create a disparity between the lim x/x as x->0, and the value of x/x where x=0.
However, given that division models iterative subtraction in the real world, why can't it be defined as the least number of times you need to subtract one number from another to reach zero? Then 0/[any value, including 0] equals 0. Seems rather impossible that, thousands of years later, it turns out we just got division wrong, so I'm assuming there's something I'm missing.
What does it break to make 0/0=0, and make multiplication and division non-inverse for that one case?
This guy is a complete idiot. You can not define the quantity 0/0=N (nullity) and at the same time use the standard rules of computation (as he does); the problem is that you easily run into all sorts of absurdity.
For instance: how much is 2*N? I might write 2*N=2*(0/0)=(2*0)/0=0/0=N, but then I get N=0 and he says this new "number" is outside the real line. So what is wrong in this computation? Nothing of course. If I decide to give a meaning to the product 2*N, and keep using the standard rules of arithmetic, I run into troubles. With some more effort I can easily get 1=0: start from 1*0=2*0, "simplify" as 1=2*(0/0)=2*N=0 et voila'.
The only way to stay clear of absurdities is to restrict the operations you can do with N; this new "number" can not interact with the other real numbers. Certainly the operations he does in the video can not be allowed. So he defined nothing new, just introduced a useless symbol for the still undefined operation 0/0
Again:
</tag> closes a tag.
<tag/> is a tag that has no content inside it (<tag/> == <tag></tag>).
So, <p/> is an empty paragraph.
factor 966971: 966971
First Kevin "Captain Cyborg" Warwick, now this nutjob. I'm starting to think it's a good idea they closed down their Physics department after all...
++ Say to Elrond "Hello.".
Elrond says "No.". Elrond gives you some lunch.
The problem with trying to abstract is that 0 holds no sign. It poses no problem when you multiply with 0, because you don't need to ask about the sign of resulting 0. However, when dividing finite with 0, you know that you have two possible and distant infinite outcomes.
Therefore, if there was 0 and -0, you could claim x/0 = (SIGN(x))*infinity and x/(-0) = -(SIGN(x))*infinity.
Perhaps nullity is used to address exactly this problem of zero's "third sign". There is also similar concept, "infinite complex number", where complex plane is mapped on Riemann's sphere, where south pole is mapped to zero, while north pole is considered "complex infinity". The nullity is "real numbers' only" version of that.
I will not accept any proof that has been released on a proprietary (realplayer) codex, where is the proof!
Real mathematician's do not teach kids until the math community has verified there proof, even if this is proved to be true i think 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.
If this is proven to be true, Then he is a lucky man.
If this is proven to be false, Then will he wipe the minds of the children he a infected with his jibberish.
Poor form, no proof other than a couple of (proprietary realplayer) movies i cannot and will not watch on my free/open os
" Ashamed to be British "
I dont get it... wouldn't it just make sense if 0/0 = infinity? I mean think about it... how many times does zero fit into zero? Infinity!
6/0 * 0 = 6 * nullity!
Therefore
42 = 6 * nullity
Look at how young those children are. At that age they already are interacting with a guy like this and are thinking about these types of problems. Damn- good job England. Those tots'll be sharp if this is the type of education they are receiving.
> His new number, which he calls "nullity" solves the 1200 year old problem that niether Newton nor Pythagoras could solve, the problem of zero to the zero power.
Oh please, what's the problem here? Every mathematical equation has an implied identity operation applied to every other one. In the case of multiplication, the identity is 1. Power works as follows: total = identity (1); Multiply total by base exponent amount of times.
Therefor 0 to the 0 power is 1 multiplied by 0 0 amount of times leaving us simply with 1.
You can be an insane coder too, read: Insane Coding
My math teacher in highschool once explained (with examples) why 0/0 is not 0, but is instead undefined (like anything else over zero). I can't remember the examples, but you could get it to be infinity, zero, four, whatever. Anyone care to post similar?
-- 'The' Lord and Master Bitman On High, Master Of All
Actually you can extend the real line to include one extra "point at infinity". Once you've done this, which takes some mathematical finagling but does actually work, you can get sensible meaning out of things with infinity as their limit. On the extended real line 1/x is continuous. I think.
qntm.org
Sure, will do. Newton devised his theory of calculus while studying motion (particularly orbits). He developed it as a way of analysing numbers, such as astronomical observations. Leibniz developed his theory of calculus while working on geometry. Both built up their theories from the work of others.
Other "natural philosophers" of the day took these theories and ran with them. Some looked to refine the mathematics (neither Newton or Leibniz did very rigorous proofs), others looked to refine the application, particularly for motion analysis (such as the newly emerging field of ballistics). Calculus turned out to be a very useful way of modelling the real world. But how real is calculus? Calculus, particularly differential calculus, is predicated on an continuous curve. Real world curves aren't continuous - they can't be; the building blocks of matter aren't continuous. But at the level we care about, we can _approximate_ the real-world curves as continuous, and apply tools and techniques such as calculus to them.
Naturally, the recognition that a mathematical concept can be a useful tool often drives further elaboration of the concept; there is a natural return on investment that drives it. But it's only a tool. Even something as simple as "1 + 1 = 2" is merely a mathematical concept that just _happens_ to be a good way of keeping track of apples.
"Software is too expensive to build cheaply"
Mod AC up, smug american (who claims in other post that s/he is a mathematician) down.
If the guy taught at the University of Math I might be curious enough to RTFA before dismissing him outright.
My mind is closed, its hinges rusty.
I used different reasoning, but I came up with the same sort of thing in high school. Then I took Calculus, and learned about limits, which are a lot less ambiguous, are actually useful, and fit into the rest of mathematics.
http://outcampaign.org/
I remember reading somewhere about some teenage kid, a long time ago, that found current mathematical frameworks to be insufficient for some new planetary motion computations he wanted to perform. He then, against all accepted scientific and mathematical norms, created his very own bizarre framework, one that did just what he wanted it to. He then called it some weird latin name, and thought it was so bizarre, he didn't even attempt to publish it until much later, when he was older. Perhaps you've heard of him?
Seriously, I'm not agreeing with this Nullity thing, but all I'm saying is that to "restructure math as we know it", sometimes happens with splendid results, and its quite more than "just being clever".
-dZ.
Carol vs. Ghost
...that Dr Anderson must have read "The Equation That Couldn't Be Solved". He got tipped off about the book by the front page of /. where the review has been prominently displayed for the past, oh, 3 years. This book review will disappear and be permanently replaced by "I Was A Computer Geek Up To His Pits In Babes" once I finish writing it. Only problem I'm having is figuring out how to be a computer geek up to my pits in babes. Makes that whole "division by zero" thing appear to be trivial.
Mr. T pitied this fool on 27 July 1992.
nice comment in the page:
Chuck Norris
I could have told you all this years ago.
What do you mean "better known as complex"? Imaginary and complex numbers are entirely different things.
A multiple of i is an imaginary number (anything along the imaginary number line), and a complex number is any combination of an imaginary number and a real number (hence, anything in the complex plane).
Besides, re: electrical circuits, it's not why they work, it just makes the maths an awful lot easier. Most of the time you switch into the complex plane and then take the real part when you need an answer. It's basically an alternative to having to use a quagmire of trigonometric functions, and the same is true of quantum mechanics.
I've got the spirit, lose the feeling.
change DivideByZeroException to NullPointerException
As you all know, Chuck Norris CAN divide by zero. He always could. Nothing new here, please move along
We often refuse to accept an idea merely because the tone of voice in which it has been expressed is unsympathetic to us
Here's one from the "young whippersnapper" department.
When I was a boy, we programmed air/space craft simultations for NASA.
Not the just abstract videogame types, but actual mechanically-linked 3D motion simulators
that jerked (jerk is a derivative of acceleration, in turn a derivative of velocity, thence a
derivative of position) human test pilots in a shaker cockpit.
Aside: the computer coding involved aviation control math models -> Ratfor -> FORTRAN-> real-time
assembly language -> custom digital I/O in the simulation cockpit, debugged via toggle switch
breakpoints set on a Xerox Sigma 9 console, later supplanted by Foonly machine efforts.
To make a long story short, the aerospace models often attempted divide-by-zero, either from
outright programming bugs or ill-conditioned equations.
So, did we then smash the test pilot into the cabin walls at a high rate-of-change?
No, the intrepid project mechanical engineers, who grokked servo mechanisms and could care less
about snotnose Unix-head punks simply used "mechanical rate limiters" to
overcome and smooth over these "divide-by-zero" disasters.
I'm telling you, even Professor Kahan's IEEE floating-point NAN nomenclature
for calculations didn't save the day for renormalizing these infinities -- how could it,
no self-respecting kernel (Unix or otherwise) has ever executed FP operations, which still
doesn't absolve integer div-zero horrors and concomitant analog duct tape patchwork
to save the day.
Absolutely. It's also possible to extend the real number system to support something else physicists use all the time, infinitesimals and infinites:s
http://en.wikipedia.org/wiki/Non-standard_analysi
http://en.wikipedia.org/wiki/Hyperreal_numbers
Once you can get your head around ultrafilters, it's really a cool system and, like complex numbers, can allow you to arrive at conclusions that you would have a hard time arrive at without them. But like complex numbers, they don't "really exist". They're just a useful model that helps us solve and understand real-life problems.
It's a divide-by-zero trap!
Quaternions have no singularities. Euler angles have a singularity at +/-90 deg elevation. EG. The vector (assuming Z is vertical axis) can be formed by an arbitrary yaw, arbitrary roll and a pitch of +/-90. Attempting to the resolve the vector back into euler angles become impossible as there are infinite solutions.
>> "Dr. Anderson is a pompous idiot."
Anderson's contribution does at least try to solve a very real problem constructively, whereas yours is a mere ad hominem attack.
So, which of the two contributors is more likely to be the pompous idiot?
According to google 0^0 = 1
According to GNU bc program : 0^0 =1
According to Windows calc: 0^0 = 1
Looks like computer world has already assumed 0^0 =1
Define it away.
Maybe im taking the author too seriously but to say a 10 year old could divide a number by 0 and someone like Newton couldnt is just stupid. That's like me yelling to people "I know that E = mc^2 and noone before Einstein didnt know about it. I must be a freakin genius"
The problem isn't that people haven't figured out ways of dividing by zero, the problem is that there are many different ways in which you could reasonably define division by zero, and they are not mutually consistent. Wikipedia lists some of them.
So, if my program does an address calculation that produces 'nullity', does that result in a 'nullity pointer exception'?
[Insert pithy quote here]
I think I'll define another, different new symbol the Errority that represents "the wrong answer". Whenever I am taking a test, I'll use the Errority as the answer when I do not know the correct answer. Since I do not know the correct answer, using the Errority is the correct thing to do, therefore I have answered the question correctly.
Actually there are only 10 axioms and a 11th that many people don't like (axiom of choice), so they use it only when really needed. Those axioms comes from the set theory and from that you can define all the fields of math and prove their respective axioms.
Much of what we use day to day is in fact definitions. For instance, this very basic form of math, defines the real numbers in terms of sets. 0 is defined as a set that contains no element the empty set, 1 is defined as a set that has one element that is 0, 2 contains 1 and 0 and so on, I don't know the exact details but you can define the hole math in term of sets alone, off course this was done once and it has been shown to behave the way we think it should behave so it was accepted and we went on doing the things that we usually do the way it is easier.
[]'s Victor Bogado da Silva Lins
^[:wq
According to video infinite (~) = 1/0 -infinite (-~) = -1 / 0 nullity (@) = 0/0 so Infinite plus negative infinite ~ + -~ = 1/0 + -1/0 = (1 - 1) / 0 = 0/0 = @ so infinite + negative infinite is a nullity not zero. Bow down to my greatness ye masses.
Here's how I explained it to my younglings:
Rebecca has 10 apples. If she divides it into 2 groups, each group will have five apples. If she divides it into 1 group, she will still have 10 apples. How does she divide the apples into NO groups?
There was a pause, and then bright look as my nephew said, "Throw the apples away."
Smart kid.
Take a look at what the man has actually written instead of some terrible news article before bandying about the "idiot" moniker too freely:
http://www.bookofparagon.com/
I'd lump him in the same delightfully fun kook category as Rudy Rucker and Wolfram (and he might just have something)...
From TFA: "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 big trouble. If your heart pacemaker divides by zero, you're dead."
"Try-catch" blocks anyone?
So say we all
it?
How does it work?
Does it keep the "you can divide by zero if you know how you got there" class of equations functional?
i.e.
lim x->0 (x/x^2)
etc.
34486853790
Connection too slow for X forwarding? Try "ssh -CX user@host"
What this professor invented, as many others notices is in fact NaN. You can add NaN to anything and you get NaN.
... :P
So this is really just a form of error handling and no use of "nullity" exists beyond detecting errors as I see it.
This is since his definition is wrong. If we want to make some use of division by zero we need to define a workable set of rules that don't conclude with "everything is nothing" and "10 = 20" conclusions which leads us to little use.
What if we do it like with imaginary numbers. We define "zero divided" numbers in a completely new dimension, and hence we can not sum, multiply or divide "nullity" with anything by definition, except "0" which then produces 1.
Then we will at least not get non-nonsensical outcomes from it, and further exploring it it may actually be useful. I'll use "N" for nullity in few examples.
First few axioms:
number / 0 = N * number;
0*N = 1;
N / 0 = N^2;
-------------------
10 / 0 = 10N;
10N*0 = 10; -> there we go, the result now makes sense
10N / 0 = 10*N^2;
10*N^2 + 20 = 10*N^2 + 20; -> i.e. you can't just "add" 20 to N since they are in different realms, this is consistent with complex numbers.
However:
10*N + 10*N = 100*N;
There we go. Now rip it apart
If I remember my 1st year calc (which was 6 years ago) correctly:
LIM x->0 (x/x^2) = 1/2
LIM x->0 (x^2/x) = 2
LIM x->0 (1/x) = infinity
and I know theres a way to get the result to be 0 also...
So, the problem is that the value of a division by 0 is dependant on how you get there, and it seems to be this isn't a very good answer. That is, unless, contrary to what the name might suggest, Nullity is actually comprised of all numbers. Then shouldn't it be Omegity?
34486853790
Connection too slow for X forwarding? Try "ssh -CX user@host"
Maybe this guy should stick to what his University has in its name: READING. Keep out of my math textbook, please!
Just idle speculation - would there be any practical use of redefining zero as the following -
1. Real zero value itself is a discontinuity in the number line
2. For practical purposes positive zero is the smallest possible positive floating point number we can assign
3. Negative zero is just the largest posible negative floating point number we can assign.
I am sure that this might be quite stupid in several ways, but my maths education was a long while back, so please excuse in advance.
Utter rubbish, as usual. Just like those idiotic programmers who start counting from zero.
Repeat after me: Zero is not a number. I didn't hear you, say it again.
Let's get this straight. A number is representative of a quantity.
Zero represent "nothing".
"Nothing" is not a quantity. It is, well...nothing.
Ergo, zero is not representative of a quantity, which means Zero is not a number.
Why is is so hard for people to understand that?
Anyway, math works with numbers, not programmers' fallacious ideas.
It's good that as a rule division by zero is not allowed. Adding this programmers' idea of division by zero would surely add a bug to the system. Yes, and some moron is bound to give us a patch, as this one just did. But guess what, it was wrong in the first place, and should be removed from any support whatsoever.
Have you read my journal today?
So what he has discovered is that you can get around problems with dividing by zero if you handle it as a special case. How can this even be news?
I just scanned over his papers. In the second paper he tries to deal L'hopital's rule, lt x-> 0 sinx/x e.g., by saying that we should not consider sinx/x to be continuous at zero. However, we can consider sinx/x to be continuos at 0 for one very good reason - the removable singularities theorem in complex analysis which tells us that in cases like this there is always precisely one function to which sinx/x can be extended so that it is analytic at zero. This theorem guarantees that these are not "harmful extensions" as he calls them but totally harmless extensions. He is a crank. All his idea amounts to is insisting that instead of referring to functions like f(x) = sinx/x as we usually do we would have to call the function f(x) = sinx/x if x!=0, but = 0 if x = 0 - which in light of the removable singularities theorem is unnecessarily clumsy.
Anyway, after reading it i need to sneeze. So should you
Lucky accident? What do you think Physics is? Physics is a Mathematical model of the real world. If you say Mathematics doesn't deal with the real world, then neither does Physics. The real world deals with knowing that if you throw an apple into the air, its gonna fall back down (and hit you on the head if you're a really bad catch.) Physics uses Mathematics to describe how the apple travels, and to describe a theory of why the apple comes back down in the first place. Some of the Mathematics that Physicists use is more complex than anything you'd find in an Advanced Mathematics degree.
I'm sorry, but the parent is total b.s., and to be given a +5 Insightful is a joke.
Check out: http://www.bookofparagon.com/ It has what seems to be a fuller explanation of this "idea": http://www.bookofparagon.com/Mathematics/PerspexMa chineVIII.pdf
My 2c: I am no math-genius, but unless he comes up with some new way to actually use this "nullity", I do not for the love of God understand what he has done that merits even 5 secs of fame...
And here's the new and interesting bit, our friend James Anderson of Reading has apparently also solved the problem of how mind relates to matter:
It is something about a perspex, which is "a simple physical thing that is both a mind and a body", "a particular kind of matrix", "a physical shape, a physical motion, an artificial neuron, and an instruction for a machine that is more powerful than the Turing machine".
It is also: "an instruction for a perspex machine that is more powerful than any theoretically possible digital computer".
And of course, "...[a] perspex machine operates in a 4D space of perspexes called perspex space." And it "can describe any aspect of the universe we live in, and can be built from any part of our universe."
Now I have actually read philosophy but that gets me nowhere with this guy. He seems to have swallowed some Leibniz and is trying to mix it with material realism, and further believes that eg. two discrete software programs can change continuously into another - while retaining the ability to use the same stored data (I am going to make miniscule changes to my OS after writing this, with a magnet, and see if it won't still be able to run my programs).
What does help me understand him, however, is having tidied up in wikipedia and this seems a case of "things made up in school" and... well, nut-job-theries.
IAIFARSIJDPOOTV - I Am In Fact A Reality Star; I Just Don't Play One On TV
"Dr James Anderson, from the University of Reading's computer science department", where does that say anything about him being a professor? UK universities don't just hand out the title 'professor' like candy. There are 11 professors (one of whom is actually retired and another who isn't a permenant member of staff) in my department out of at least 30 members of academic staff. (there are 19 other people listed as academic staff, but I know of at least 3 people listed elsewhere on the staff page who actually teach stuff).
Do real numbers or infinite sets actually exist? When you get down to the concept of existence it's a little tricky. The models, in a sense, are our reality, because that's how we impose structure on the world.
This is a LIGHT BULB JOKE. It may be only slightly funny, and it certainly isn't "insightful", but it's not a troll. It's a JOKE.
0^0 = 1/2
Zero to any power is zero (0^x = 0)
Any number to the zeroth power is one (y^0 = 1).
We have a conflict. According to one equation, 0^0 is zero, and according to the other, 0^0 is one. The only fair solution is to split the difference. Therefore 0^0 = 1/2.
There's nothing to see here, people.
If "disco" means "I learn" in Latin, does "discothèque" mean "I learn technology"?
i = +SQRT(-1) AND i = -SQRT(-1)
Therefore:
+SQRT(-1) = -SQRT(-1)
2*SQRT(-1) = 0
i = SQRT(-1) = 0
i = 0
There you go! Hawt dang, am I smart!
You know, there is a difference between trolling and pointing out the flaws in your reasoning. Just saying.
My calculus class always used to divide by zero... just for very large values of zero.
Also known by the more polite terms NaN and Undefined, 0/0 and cousins are also the basis of pseudo-proofs which abuse the unwillingness to "just let it go". Then you can "prove" that Intelligent Design is more valuable than evolution and lots of other neat things, like perpetual energy generators.
If this were 100 years ago, the variant would be inventing some straddling constants when physicists couldn't get around wave/particle dualities and uncertainty.
Finally: No attempts to "imagine what it would be like" are valid if crushed by formal proofs.
My first Journal Entry ever, in 8 years! http://slashdot.org/journal/365947/aphelion-scifi-fantasy-horror-poetry-webzine
I think it would be much more interesting to define a math that did not allow any infinites. Such a math would probably be a much better fit to our real world than the currently used math systems that mostly allow infinites and continous stuff. We live in a world of limits. Physics also show (to my understanding) that you cannot go on dividing matter indefintely - sooner or later you end at particles that cannot be diveded any further and then you have a lower limit. If you look out to the universe there is also a limit to how far out we can get (see): around 15E9 lightyears. You are going to use very big numbers and very small numbers, but countably amounts.
He might as well have said the answer was 42
[alk]
Based on his wow site I would be willing to bet that this man has never written any serious amount of code. Juts a feeling ... but I would not expect him to contribute to your calculators source code anytime soon.
Infinite time means everything that can happen, will. You being you is absolutely incidental. You do not exist.
Now, I don't know much about programming pacemakers, but I imagine if it tries to divide by zero, you might already be dead.
Are you referring to L'Hopital's Rule? I believe 0/0 can come out to any number. Consider sin(x)/x, in that case 0/0 (x = 0) is equal to 1. How about (x-2)/(x^3-8). When that is equal to 0/0 (x = 2), the value is 1/12. But L'Hopitals makes assumptions as to the continuity of a function (which I believe another responder was referring to) since it involves taking the limits of derivatives.
Remember this classic phallacy:
1=2
It's all based on the inability to divide by zero. Now that we can, well....
I am the penguin that codes in the night.
It's always seemed to me that the number zero and the number infinity are incomplete. They almost need a coefficient to mean anything significant.
Take for example two very simple functions: f(x)=3x, and g(x)=2x. If you were to divide f(x) by g(x), you will almost always get 3/2. The only possible exception is for x=0, where it produces a 0 divided by a 0. You can work out this kind of thing with limits, and it will come to 3/2, but as far as the maths I've experienced admits, x cannot actually equal zero with that particular expression, only approach it. What you have done is taken two simple linear continuous functions, performed a very simple operation on them, and you produce a non-continuous function. It doesn't make sense.
You can multiply anything into zero and still get zero on the other end, but is it exactly the same? If I put zero into f(x) and g(x), they both produce zero, and when you divide, you seem to cancel out a common "absolute" zero out of the fraction, and you are left with 3/2. I think the problem of zero (and infinity) needs to be solved by symbolising "absolute zero" (or "absolute infinity") and simply applying coefficients (and working from there with more complex problems). Does anybody have any experience with/other half-baked theories about this kind of stuff?
You know, there is a difference between trolling and pointing out the flaws in your reasoning. Just saying.
5^0 = 1^0 = -1^0 = -5^0 = 0^0 = 1.
I never thought this was a problem.
(Realmedia / 0) = Nullity
Nullity = Bullshit
.
. . Realmedia = Crap
We all knew this already.
It seems obvious to me that 0 goes into 1 an infinite number of times (with a little room left over).
Therefore: 1 divided by 0 = infinity + 1
To wit: 0 = infinity!
That's at least as logical as anything in this article.
I admit to not having read EVERY comment in this thread, so it is possible this is a dup but ...
... 1/-.5 ... 1/-.1 ... Is an stream of negative numbers increasing in absolute value e.g., -1, ... -2, ... -10, ... So as you take the limit of division buy zero from the negative side it goes to negative infinity. Now try:
... 1/.5 ... 1/.1 ... and get a stream of positive numbers approaching positive infinity.
:).
The guy is wrong. The reason divide by zero is undefined is simple:
1/-1
1/1
Try a graph.
Now explain how a single number/value/nullity can represent BOTH positive and negative infinity. Maybe if I create a function that approachs positive 5 from one direction and -5 from the other direction I can coin the 'fivish' as the solution and get my 15 minutes of fame as well.
Ah well, America seems to own crappy science these days I guess the Brits are entitled to crappy math
Dr Anderson is a godam SOCIALIST. Why? Because he wants ALL division calulations to have an answer. Socialists demand CONSISTENCY at all costs. The individuality of sums like 0/0 and -1/0 (what about 1/(-0)?) must be CRUSHED in his dystopian vision.
His FLAT and SOULESS concept of numbers, in which the cold metal boot of COMMUNISM stamps down on the natural emergent topology of the real number system, is really based on a tissue of lies, daydreams and myths like all LEFTIST ideology.
The freedoms such as assciativity and distributivity upon which we depend in our EVERYDAY LIVES are hijacked by Anderson's BIG BROTHER ALGEBRAIC SPACE in which only Anderson himself and his cronies can decide what the hell (1/1 - 0/0)*3 - 0 evaluates to because only they know best... IN THEIR OPINIONS AT LEAST!!! NOT MINE!!
I am tired of all of these illustrations discussing what "0/0" is.. based on the mathematical definition of a Ring with unity.. there is no inverse for the "0". By definition, 0*a = 0 for all a.. but there is no 0^-1 thus 0*(0^-1), or as so many like to write "0/0", makes no sense. AND, it makes no sense to say a*(0^-1) either.
If you want.. you can say 0^-1 exists. Then, that requires 0*(0^-1) = 0/0 = 1 based on the rules we've given to a Ring with unity. Ok.. but.. also, 0*(0^-1)=0*0*(0^-1)=0*1=0.. so.. it's just gibberish. You cannot fit it into the system since assuming 0-inverse exists gives you 0=1
So.. for the fuck of it.. you can say, "I like to think of zero-inverse as the closure of the set of a Ring with unity.." i guess.. since it seems to have a more topological meaning but.. it makes no sense to try to utilize it with the ring operations. Or, if you want to use it, then you made R into something besides a Ring.
assigning an arbitrary symbol to a long-held mathematical idea is in no way grounds for praise. I have come up with a ground-breaking exciting new math theory too. from now on I'm going to use the symbol "i" for the square root of -1. Or, better yet, I'm going to use the symbol ^ to represent the answer to the origin of the universe. WOOHOO! I just discovered the secrets to existence. existence = ^ can I get a medal now?
Actually....
e =~ 2.781
Small caps E is used to signify y×10^x; i.e. 7e8 is 7×10^8 or 700,000,000. (Source wikipedia)
E is 14 in hex as already pointed out.
It's math, you are allowed, heck, required, to be pedantic.
And this professor is full of it.
You can define 0/0 to be nullity, NAN or whatever. It will still be intractable because any operation on nullity will have to result in nullity. Or else you would be able to define 2=1 as already pointed out.
And any limit comparisons will not change that. Limit != ==
lim
I do not believe in karma. "Funny"=-6. Do good and forbid evil. Yours, Oft-Offtopic Flamebaiting Troll.
What he did was come up with a proof of NaN. Which is different then saying "We have create an exception called 'NAN' for this case.
Much like gravity: it has always existed, but that didn't some guy from coming along and proving it existed.
However, I wuld like to here from some actually mathmaticians about nullity.
The Kruger Dunning explains most post on
This is total bunk. Hey, I created a number! It is all the numbers! Stretching from negative to positive infinity! "It was confusing at first, but I think I've got it. Just about," said one pupil. LOL!
I'm going to take a long coiling dump on the floor- whatever symbol it makes will represent the result when you multiply any number times nullity.
That gives 0/0 = 0 and 1 at the same time.
Quantum algebra? Just accept that a variable could have multiple values until inspection/application forces the 'quantum field' to collapse to a single value. Works in physics for Schrodenger's Cat, how about in math for Schrodenger's X?
Can we get a "-1 Wrong" moderation option?
There is a branch of mathematics that is intended to handle infinitesimals in a more rigorous way. This sounds like a related idea. Google for "nonstandard analysis"
Of all the media players that do not have spyware and don't take up a bloated process load, why real player? Are there any links to formats that will work with Media player like .wmv, mpg, etc?? I'd appreciate it!
Previewing comments are for sissies!
if 1/0 = inf then 0 * inf = 1 Is that very bizarre or am i not living in the real world where this kind of thing is normal? o_O
So what, the software I write commonly attempts to divide by zero.
I think this is just re-naming the problem to something else... then again, if you really think about the basics of division, the problem of division by zero comes into being because of the idea that zero is not really zero, but a really, really small number. So maybe the solution this problem should be to define zero as being trually zero (ZERO), nothing, zilch, nada!
Now if you look at division this way, lets say you have an apple (thinking of Newton) to be divided among 2 people... each gets half. Now if you divide the apple between ZERO people, what do you get? I beleive its the whole apple... so dividing by true zero is the number itself!
I read most of the comments above me, but I didn't see any mention of this. Nullity is a term used in linear algebra to describe the dimension of the null space of a vector space. It isn't as widely used as rank is; however, it still exists.
I'm not defending the nullity guy or anything, but wouldn't his new number mean that the "a + b = b" step is really just "nullity = nullity"?
This, of course, leads to the question: What is the fucking point of nullity?
The "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 have an error in that situation if that's what you want. Replacing the error condition with a new symbol accomplishes nothing. The program still has to deal with the result in some order to present a real-world result to the user. A divide-by-zero error is the way programs do that.
It's easy to solve 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 artificial solution - but the problem was artificial in the first place.
We've all run 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 or not catching and handling its errors. We've also all run into programs that attempt to reference a null pointer. By the same reasoning, we could define the memory that a "null pointer" points to as some new type of virtual space called "nullspace" (trekies should appreciate my resistance to the temptation to call it "subspace"), and call it valid. Make the computer such that reading from "nullspace" always returns zero. Suddenly no programs crash from dereferencing a null pointer any more. It doesn't mean that the program is going to now do something useful. It probably means it will end up displaying garbage to the user, hanging in an infinite loop, or branching off to never never land. It seems as if Doctor Anderson is making a value decision about the error report that calculators and errors report. It's an error, and that must be bad so it needs to be fixed. It's a feature, and intended to assist in writing good software.
Now as far as it goes mathematically, that's even simpler to address. There's nothing you can do with nullity on paper that you can't do 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 help my opinion. You can read this as the fourth comment after the BBC story. Tossing out the names of two other Ph.Ds and offering vague references to undescribed "axioms" built around this new symbol all reinforce my opinion that Doctor Anderson sounds precisely like the character Robert from the movie "Proof". A tale... full of sound and fury, signifying nullity.
Uhm... Or actually. I generally use /dev/null for that to begin with...
*ponder* So what *is* the use of this? Considering that for example -O- - -O- would end up being 0, -O- * -O- would be -O- and -O- + -O- = -O-....
Hmmm... That looks deceptively like the behaviour of the number 0, with one small exception, and that should be -O- / -O- which would be 1. - -O- / -O- would then be -1? Okay. I'll quit rambling now. See my subject!
Splut.
Coz eternity my friend, is a long *ing time.
Zero doesn't have a sign, but limits to zero _do_ have a sign, plus, or minus, or plus-or-minus. The limits to 0+ and 0- are convergent limits (the + and - at the _end_ of a number, like 2+ or 2- mean the limit is reaching the number from above or below, and in the case of 0+ and 0-, since "above 0" is positive, and "below 0" is negative, we have different signs). The limits to 0 (with the sign unknown) does not converge (meaning there are multiple results).
Given lim x -> 0+, then 1/x = +inf and Given lim x -> 0-, then 1/x = -inf
Given lim x -> 0 (that is, the sign is "unknown"), then 1/x = { -inf, +inf } -- yes, _two_ answers, just as the sqrt(4) = {+2, -2} whereas |sqrt(4)| = +2
Thus, assuming that 0 = { lim x -> 0+, lim x -> 0- }, yes, we're saying that 0 is of 2 values (one positive, one negative), then 0^0 has 4 possible values, 0+^0-, 0+ ^0+, 0-^0-, 0+^0+. Now, if you work out the limits, you'll see that 0+^0+ converges to 1-, that 0+^0- converges to 1+, that 0-^0+ is... well, I don't have a complex calculator (I'm using perl to plot the curves), but if you work out the math you'll find that it's a complex number which, probably, has a real component that converges to 0 or 1 from above or below and an imaginary component that converges to 0 or 1 from above or below, or a trigonometric function thereof.
This story has reminded of my 11th grade high school class. We had this international day, where people would share their heritage. For math class, we were supposed to write the numbers one through ten in the language of our homeland.
Having no homeland to speak of, I made up a language and numbers. Just jibberish.
Except for the number nine. It was spelled n-i-n-e. I don't know why, but the fact that every other number was jibberish but my 'homeland' spelled 9 the same just cracked me the fuck up.
Days Later, they had a spiffy bulletin board up, and sure enough, on the board in big letters was one of my fictitious digits.
I laughed my ass off for a good 20 minutes, and nobody in class knew why.
"Was it a millionaire who said 'Imagine No Posessions?'" -- Elvis Costello
since when do pacemakers divide by anything?
Oh Crap, I'm an optimist.....
Nietzsche has always been right, we will all become Übermenschen through this revolutionary theory. Of Nihilism.
Too bad it's based on nothing
Division is the act of repeatedly subtracting the denominator from the numerator until the numerator is less than the denominator. Thus, clearly, x/0 is infinity for positive x, and -infinity for negative x, for both integer and real numbers. Further, by definition, 0/0 is clearly _any number at all_ -- you can give up whenever you like. Consider the graph of the tan function. At the asymptote you are effectively dividing by zero. I fail to see the benefit of declaring the value NaN or undefined, outside the computational capabilities of a given set of computational hardware. It's clearly a continuum of every possible number between + and - infinity, rather than the traditional discontinuity, in my view.
-- "Quis custodiet ipsos custodes?" -- Juvenal
Only Chuck Norris can divide 0!
Complex numbers are useful becuase they are useful in equations and can be used to generate real answers.
I've read his "technical" paper and all it says, in a lot of mathematical jargon, is that once you divide by zero anywhere in an equation the result is 'undefined' only he has now given 'undefined' a new mathematical symbol and a funky name.
Unlike an imaginary number which can give a real single value when used in an equation (e.g. 2i^2+4 = 2) once you divide by zero anywhere in an equation you result can be anywhere in an undefined space between infinity and negative infinity. He calls this space Nullity
So his invention is actually not a mathematical one, it is a gramatic one. Nullity = Undefined, Undefined = Nullity.
Quantum Physics a.k.a. sub-molecular statistics
He's not invented a false reality, he's developed a new, more complete, system of arithmetic. Mathematics is not the study of reality.
As to not solving any problems: It makes things which were previously impossible to calculate possible to calculate. It solves the problem that previous systems of arithmetic either failed to define the result of divide by zero at all, or failed to define it in a useful and rigorous fashion. Whether you think the problem it solves was serious or the solution is a good one is a different matter.
Chernobyl 'not a wildlife haven' - BBC News
a * x = 0 [ + a [ + a ...] ] for x repetitions of a. When x=0, there are NO a's in the right side of the equation, and the result is simply 0. It doesn't matter if a is positive, negative, or zero, because there are none of them in the expansion.
a ^ x = 1 [ * a [ * a ...] ] for x repetitions of a. When x=0 there are NO a's in the right side of the equation, and the result is simply 1. It doesn't matter if a happens to be 0, because there are no zeroes in the expansion.
The professor was all hung up over the fact that a ^ x is discontinuous at a=0 and x=0. But 0 ^ x is already undefined where x Then there's this putz, who thinks he can rename NaN and do something meaningful with it. The reason why division by 0 is undefined is because ANY number can be multiplied by zero to produce zero, and NO number can be multiplied by zero to produce anything BUT zero. Numbnutzity doesn't add anything of value to mathematics. But thanks for playing. Johnny, tell him about the nice consolation prizes....
[100% ISO 646 Compliant]
SVM, ERGO MONSTRO.
dude, i just figured out how to use my speak 'n spell, now you want me to divide by ZERO? http://popculturepundit.com/
Let R be the set of real numbers and define R* = R U {0*} with the following properties:
1) a/b = c for some c in R if and only if b ~= 0,0*.
2) a/b = 0* if and only if a = 0 and b = 0.
3) 0*/0* = 0*
But without careful definition, R* may not have the same topology as R, which means that calculus won't work as expected. That's the real test as to whether or not this prof has come up with something interesting.
2. post it to news sites
3. profit!
No, I think you messed up somewhere.
1. Invent something amazingly useless.
2. Post it to news sites.
3. ???
4. Convince mathematicians it's not a stupid idea.
5. Profit!
Saved By Zero just became a better song.
Somehow I think this guy has solved a 1,200 year old problem by creating yet another one. If this nullity thing equals 0/0, then what does nullity+nullity equal? How bout nullity^2? So when are we going to solve the problem of doing basic arithmetic on nullity?
>He's not invented a false reality, he's developed a new, more complete, system of arithmetic.
Isn't that something every mathematician does several times on the way to a Ph.D.?
"Inventing more math" is the math equivalent of "Inventing more grammars" in the CS realm.
Doing so does not change the landscape for existing fields of math, any more than writing a language like Befunge changes other grammars.
-fb Everything not expressly forbidden is now mandatory.
Check out Geometric Algebra. It integrates quaternions and vectors in a way that makes sense. The two together are greater than the sum of their parts.
Hofstadter's Law: It always takes longer than you expect, even when you take into account Hofstadter's Law.
what is the application of this into real world problems. furthermore what will happen when the ecu on my car is only nullity 1.0 compliant and tries to divide by nullity 1.2.1.3alpha2.
lose != loose
So this PhD in Computer Science says, "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 big trouble. If your heart pacemaker divides by zero, you're dead."
Where did he get his degree, exactly, that he doesn't know how to catch exceptions? Hell, I learned that in CS1!
I can think of other words ending in -ity. the most appropriate one starts with s.
“Common sense is not so common.” — Voltaire
The solution is: #DIV/0!
Random rants about technology: http://technorants.blogspot.com
The limit of c/x as x->0 (from a complex direction) yields a directional infinity.
They look like the form (a+bi)*inf, where (a+bi) is on the complex unit circle.
If you don't specify a direction, then the limit does not exist.
The function c/x doesn't have that smooth neighborhood property at x=0, but it's differentiable, or something like that. (Help me out, math majors, I didn't take complex analysis)
THIS THING CAN TURN ON A DIME, MACROSSZERO STYLE ALSO FUCK BETA, ~NYORON
Y'all are nuts for even bothering with modern math ... the guy at timecube.com figured it all out and published a proof of reality years ago.
Mathematical constructs that describe the real world are useful, no matter what bias or misnomer (eg. "imaginary") is applied to them.
Patrick Doyle
I mod down every jackass who puts his moderation policy in his sig. Oh, wait a sec....
If you look at the history of math, it's always leaps of stupidity like this that were responsible for actually improving and extending mathematics. Start with the number zero. People said zero doesn't exist, so it's not a number etc. Then people took note of it's special properties and started playing around with it, and lo and behold we went from roman numerals to arabic numbers, making something like multiplication much, much easier.
Most other big innovations were caused by people doing what was supposed to be avoided. Wherever "things got fuzzy," that's where big changes occurred. Think of calculus, which is only allowed by accepting Zeno's paradox, ignoring the drama, and focusing on what can be manipulated mathematically.
Well, I have no idea. Personally, I saw the article and went "WTF, I could have done that." It really, as far as I can tell, doesn't do anything special. Besides, due to L'Hospital's rule, 0/0 can be, well, anything.
He introduced a multiplicative inverse for the additive identity (0), and added it to the real number field.
Unfortunately, he just complicates things, because he doesn't define how the + and * operators map up with it (nullity + a = ?)... if he doesn't then he breaks assoc/commu/trans properties (no longer a field then). And of course that number we need additive/mult inverses which may require nullity-prime, and so on, and he's just going in circles.
THIS THING CAN TURN ON A DIME, MACROSSZERO STYLE ALSO FUCK BETA, ~NYORON
You can hide it, but computers count from zero...
And he will be pretty mad when he hears about this.
Your second sentence does not follow from the first.
The limit notation can successfully be used with infinity. For example: lim[x->0] 1/x = infinity. The fact that the limit is infinity does NOT mean that infinity is considered to be a real number.
In addition, a real variable is allowed to approach infinity, so we can also say: lim[x->infinity] 1/x = 0.
A trivial counter-example to your statement can be seen in sequence of natural numbers: 1,2,3,4,5... . The limit of that sequence is infinity. That fact in no way means that infinity is a real number.
Mathemeticians have allowed infinity to be used in conjunction with several notations: limit, summation, and integral. In each case, there are clear rules that restrict exactly where infinity can appear in the notation. In all cases, the infinity is kept strictly segregated from real values.
I have 6 apples, Tommy and Sheila both want an equal share, how many apples do they both get? 6/2 = 3 I have 6 apples, nobody wants any apples, how many apples does everyone get? 6/0 = 0 And I get an upset stomach from eating so many apples myself...
Read his papers... or attempt to.
He thinks that by adding nullity he is 1) keeping the reals a commutative ring while 2) turning multiplication over reals into a group.
Of course, nullity is not in the group. This just moves the goalposts. In fact, I still don't think multiplication over reals (using the definition of but excluding nullity) is a group anyway (haven't look hard for a contradiction, there's gotta be an easy one), so what's the point?
THIS THING CAN TURN ON A DIME, MACROSSZERO STYLE ALSO FUCK BETA, ~NYORON
You're exactly right. When you've got the limit sign, and a directionality of approach and everything, it's all good, you get a quantity. The value of the limit is wrapped up in the expression that approaches it (this is where the "constant" came from).
But you can't evaluate the expression AT ZERO, that's ludicrous. The function is continouous with a hole, and that's just the way it is.
THIS THING CAN TURN ON A DIME, MACROSSZERO STYLE ALSO FUCK BETA, ~NYORON
Yes, that's numberwang!
We have undefined because it means that our assumptions (in the expression leading up to it), were FALSE under the axioms of our proof system. (Either your assumptions were wrong or you forgot a few special cases of (f(x)!=0) somewhere). Calling it nullity and plowing ahead would completely invalidate anything you were trying to prove in the first place. Often times in mathematics you assume the converse is true and find a contradiction to show the original statement must be true, good luck with that after nullity. Mathematically useless.
THIS THING CAN TURN ON A DIME, MACROSSZERO STYLE ALSO FUCK BETA, ~NYORON
Just to set you straight, that guy's a total zero.
All this guy has done is redefine what the real number line is and a few numbers. Let's go 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 we approach 0 from the left then the sign flips. But that's another story.
What he did was an operation that was undefined.
This guy is playing with a NEW number line of his own invention. Also, this NEW number line has not been shown to be mathematically consistent in any way shape or form.
This guy is a mathematical moron and he should be embarrassed to publish this.
I guess that math degree of mine has proved itself handy after all
I just told the wife (PhD in Physics) and she has informed me that this happens in her field as well. Basically, Engineers learn a little bit of physics, think they know what they're talking about, and come up with "better" alternatives to relativity, etc. This apparently is what happens with the Comp Sci people as they learn a little bit of math, and think they come up with "solutions" to math problems.
I honestly think that it'd be best if we'd all stick to basically our own major subject domain.
He didn't solve anything at all... When mapping the real number line it isn't a straight at all. Zero is effectively 1/infinity or -1/infinity. In Einsteinian / Hawking style math / physics, the concept of infinity will warp space-time or in this case the number line. On the number line infinity will bend back around to zero (one/infinity). By stating nullity is 0/0 is no different than stating just zero. Zero is a concept not a number.
Dividing by zero is never defined. x/0 is NOT EQUAL to +/- Inf, no matter what your calculator or computer says.
The limit exists, sure enough, but the limit takes directionality in account in the expression, which is where the sign (or complex directional infinity) comes from.
Please don't misuse limit expressions and perpetuate falsehoods about our precious additive identity!
And zero isn't signed. By definition. Now, the construction [-0.00000000, +0.00000000], the bounds which define the real number zero might look like +/-, i.e. signed zeroes, but they two are really just limits with direction, and the value of the limit (i.e. 0) has no sign. At all.
THIS THING CAN TURN ON A DIME, MACROSSZERO STYLE ALSO FUCK BETA, ~NYORON
In his case, he didn't introduce a "catch-all" symbol, he introduced classes of infinities (ordinal and cardinal) with constructions and everything... it was actually useful for stuff.
This nullity is... well.
THIS THING CAN TURN ON A DIME, MACROSSZERO STYLE ALSO FUCK BETA, ~NYORON
Division by zero SHOULD be an exception:
Either...
1) your model is wrong mathematically
2) you translated your model into code incorrectly
3) you have an off-by-one bug
4) your model is ill-conditioned and underflows
5) you're not handling precision correctly
6) you need arbitrary precision
It's one (or more) of those things when you get that DIVIDE BY ZERO exception and your program crashses. THINGS THAT SHOULD BE FIXED. Fix the code, don't wrap it in a class and hope it doesn't happen again!
THIS THING CAN TURN ON A DIME, MACROSSZERO STYLE ALSO FUCK BETA, ~NYORON
i think it is wrong, given his axioms (as defined here: http://www.bookofparagon.com/Mathematics/PerspexMa chineVIII.pdf).
(inf) = 1/0 [A20]
= 1/(-1 * 0) [T77]
= -1 * (1/0) [A13]
= -1 * (inf) [A20]
= -(inf) [A24]
which contradicts his axiomatic supposition of (inf) and -(inf) as unique entities [T41]
lysergically yours
(jerk is a derivative of acceleration, in turn a derivative of velocity, thence a
derivative of position)
It's been a few years since my physics days, but I'm pretty sure velocity is a derivative of acceleration, and position is a derivative of velocity.
Microsoft is to software what Budweiser is to beer.
Working from his proof:
0^0 = 0^(1-1)
0^0 = 0^(1)*0^(-1)
0^0 = (0/1)*(1/0)
0^0 = 1
Therefore 0^0 = 1, or what I'll call Uniplex, which coincidentally will look like a capital phi.
Please contact me for information on where to send my Fields Medal.
How many lines does this post have?
"one could technically define a set of numbers which includes +=infinity"
Technically you could not do this. Remember, infinity is not a number, it is a concept meaning an unbounded limit. There are rules for including it in algebraic equations, but it is still not a "number."
The TRUE Libertarian would sit in the dark until the Free Market came up with a solution :-)
My apologies if you are receiving multiple copies of this call for papers.
We invite new and innovative submissions for an upcoming symposium to discuss the novel concept of "nullity". "Nullity" was first proposed by Dr. Anderson when he was teaching schoolchildren in 2006A.D. (the actual inventor is still debated). However from that time onwards nullity has been used to prove many phenomenon in everyday life including debt reduction, break ups and even vasectomy. The manuscript should be novel and not published elsewhere. The area of interest includes but is not limited to:
Nullity in network design
Nullity chip design
Evolutionary nullity
Educating children on nullity
Nullity based algorithms
Please submit the above papers directly to Dr. Anderson at an.ders.on@__.__ (Please install the nullity plugging to display email address). The symposium will be held from 29-35 March 300G.E. on First Foundation.
You're right of course. I was too fast with my reply, and now it's archived for all time.
Idiot mathematicians have been failing for years, but the problem is their efforts have been conducted at 1 atmosphere and room temperature. The round edges of the null digit can't cut ANYTHING under those conditions.
tone
tone
I think the problem with your example is that the model you propose is human-centric. From my perspective, the value of the bill is $10, regardless of us knowing about it or not (because the truth exists even if you don't believe in it, or don't care about it).
Here is another one:
- imagine that there is a rock lying on the ground,
- let m1 be the mass of the rock after it was seen by one person
- let m be the mass of the rock when it is not seen by anybody
is m different from m1?
Where I'm getting at, is that the universal laws of physics 'claim' that $10 bill (even though it only has a meaning for us, while for the universe it's just a set of particles)
The saddest poem
fans of 1998 or 1999:
i on+by+zero&ie=UTF-8&oe=UTF-8
..."
http://www.google.com/search?q=uss+yorktown+divis
"Windows Crash - USS Yorktown Dies Due to Divide by Zero
USS Yorktown Dies Due to Divide by Zero Posted on Sunday, September 15 @ 19:32:14 EDT by coppit News articles of interest The Navy's Smart Ship program is
www.windowscrash.com/modules. php?name=News&file=article&sid=1 - 23k -
-----
Lots more where that came from....
Hopefully we don't have any ms programs built into shipboard defence systems...
(captcha: "reflects")
Previously: "Linux... Toward the Sunrise..." Now: "Linux... Toward the-- No, now, part of Every Sunrise"
I thought that this had been around for a long time. At least one system I use (R) has used NaN in almost exactly the same way as this nullity for years. e.g.
> nullity<- 0/0
> nullity
[1] NaN
> nullity + 2
[1] NaN
> nullity / 0
[1] NaN
> 1/0
[1] Inf
> Inf - Inf
[1] NaN
> Inf > 0
[1] TRUE
> Inf + -Inf
[1] NaN
The only difference that I can see is that it returns NA instead of NaN for some operations, e.g.
> nullity > 0
[1] NA
This Prof will be busy working on Nullity/Nullity=? Nullity*Nullity and (Nullity)^(Nullity)=?. What a serious research topic...
This is like 1st grade math.
He has introduced an algebraic object that is not a ring or field, that is only different notationally compared to IEEE Inf/Nan semantics (aside from NaN != NaN).
What problem is trying to solve with these constructions? It certainly won't make arithmetic any more or less sound... dividing by zero is a problem of phrasing the question, rather than the semantics of the representation of the answer.
An example:
Suppose we have, through some process, yielded an expression f(t) = g(t)/h(t). The end result of f(t'), let's say, is 5.
And let's say we have an additional piece of information, g(t) = 10.
Then we can deduce h(t) = 2, and perhaps determine either g^-1 or h^-1 with additional information at data points (t_1, t_2, etc.)
Now let's say f(t') = nullity.
So, h(t) is 0. Or maybe not, because g(t') might be nullity at t'. If we knew h(t') is neither (0, nullity) then we know g(t') is nullity.
And if h(t') is 0 or nullity, then we can't determine what g(t') is... it could be anything.
The data point where the answer is nullity gives us no usable information, other data points (t_1, t_2) must be considered.
The same would happen in the first example if h(t') = 0; that datapoint t' would not be possible, a t' not in the domain of f(t).
This example might seem silly, but my point is that the nullity doesn't really tell you very much, other than that you propogated forward a division by zero and it collapsed your quantity to the number out of the number line. It's a unexceptional exception. It's like NULL in an outer join or normalized representation... not a good sign.
But in any other system, you would either have a contradiction, or in the case of software, an exception, which is just as valid in determining how to handle the situation, or to work around it.
THIS THING CAN TURN ON A DIME, MACROSSZERO STYLE ALSO FUCK BETA, ~NYORON
True enough. Even the definition of integers is pretty abstract. 3 is defined as {{{{}}, {}}, {{}}, {}} under the set-theory definition, which I believe is the standard one these days. The definition of irrational numbers using Dedekind cuts is even more abstract. It's hard to ascribe anything even remotely resembling concrete reality to these things.
From the whiteboard:
infinity = 1/0
-infinity = -1/0
nullity = 0/0
0^0 = 0^(1-1)
= 0^1 * 0^-1
= (0/1)^1 * (0/1)^-1
= 0/1 * 1/0
= 0/0
= nullity
my mistake.
[T81] guards against this.
carry on.
lysergically yours
Professor Chuck Norris
-- Watch me working: www.magerquark.de
.. in which case, how do I jump off the number line and into abstract mathematics? Its all good for assigning a Nullity - which, in Computer Science atleast, has existed as a concept for a long time - but try solving some more interesting mathematical proofs using it. Another thing which strikes me as suspicious - where is that paper which is going to be published in 2007? Most people release drafts, and in this case, its a paper for Nature which doesn't strike me as something which should be regarded as secret to begin with. No matter which journal you submit a paper to, atleast give the masses some sort of a mathematical idea to balance and probably and even comment on. Not everyone has the patience or the penchance to sit through a RealPlayer video. I wish someone would put it on Youtube..
If Bill Gates had a dime for every time a Windows box crashed...oh, wait a minute - he already does.
"Our mission is to develop hardware and software to bring you fast and safe computation that does not fail on division by zero. We also promote education and training in transreal computing."
Their first act will probably be a patent: "A system and method for division by zero".
If I listed this problem on my http://www.mathpotd.org/ (Math Problem of the Day), should it go to K1-2?
Hand this guy a potato sack for clothing and a shopping cart for his belogings. Then send him and his other voices on there merry way. But really, anyone that has studied topology at all can see the stupidity in this. - SPT
The computers are just doing 0^0 = exp(0 log(0)) = exp (0) = 1. The problem is that log(0) isn't really defined, so this is nonsense.
Yes. This is correct. Divison is defined as the inverse operation of multiplication. In the cases where other ways of thinking about it (splitting a pie into n pieces, for instance) don't give any kind of reasonable answer, you go back and look at the definition. The definition is very rigorous and exact (comes at its base from ZFC (Zermelo-Fraenkel with Choice), and is a part of Peano Arithmetic), and one of the consequences of that definition is that division by zero is undefined.
SIGSEGV caught, terminating
wait... not that kind of sig.
I didn't see anyone else ask this, but whats X/nullity?
Also whats nullity/nullity?
Did he define that in the research or did we just "solve" an old problem with a solution that implies a new problem?
Hello. I don't know if you have email alerts on, so I'm not sure if you'll even get this message, but I would like to ask you a few questions about studying mathetmatics (I'm a 15 year old student that's very interested in pure math). If you're willing, please contact me at pingu.design[AT]gmail.com
If you can't code for it then it can't exist. Enjoy.
This ain't no upwardly mobile freeway This is the road to hell
- Company is founded in 1980
- Celebrates "1st anniversary in 1981"
- Celebrates "2nd anniversary in 1982"
- Celebrates "3rd anniversary in 1983"
- Celebrates "4th anniversary in 1984"
- Celebrates "5th anniversary in 1985"
- Celebrates "6th anniversary in 1986"
- Celebrates "7th anniversary in 1987"
- Celebrates "8th anniversary in 1988"
- Celebrates "9th anniversary in 1989"
- Celebrates "10th anniversary in 1990"
So what's the problem?
Build a man a fire, he's warm for one night. Set him on fire, and he's warm for the rest of his life.
At first I thought this must be at least equivalent to infinitesimal analysis, or taylor series expansion and taking limits, but after reading TFA I realise it's not. The axioms he presents are simply the NaN axioms, and they still lose information just like the "standard" axioms do. Loss of information is the thing that limit analysis avoids in order to get sensible answers near zeros, but even that doesn't work for some non-smooth functions. Anyhow, he suggests implementing his axioms to replace the IEEE axioms, but if you did that you would still lose information when multiplying by zero and such, so that later divisions by zero still give you NaNs, and you haven't gained a thing. You get practically the same result by simply ignoring floating point exceptions on current hardware! His assertion that this would improve the floating point model by avoiding these problems is therefore false.
Music speeds up when you yawn, but does not change pitch.
Skysaber that fantastic fanfic fantasist also known to the world as Jared Ornstead was lambasted when he wrote a little ditty in his fanfiction.net account on how to divide by zero.... Of course some of the overly religious statements he made at the time probably didn't win him any friends either, but here at last in the work of Dr. James Anderson he is vindicated!
So ummm.... Skysaber? How about an update or three? We've been waiting since like forever!
...my system panic'd with a SIGFPE...
one thousand is 1 nullity nullity nullity?
odd, i was taught 0 is pretty much null,..well treat it that way and you wont get problems.
quick! hide the stash! put it in null!
*stash goes into null*
later that day,wheres the stash?
in null
oh, well im not getting it.
The reason one can't divide by zero, is that one can't divide by zero. Limits and precalculus are another thing. Though i is imaginary, it's possible that one could produce i squared, which is 1 and real, and it also possible for limits to converge, but limits are not arithmetic, and
in arithmetic it simply can't be done, having a divisor is a requirement. Imagine if you have five apples, and you want to share them with your
3 friends , one can cut all the apples into 3rds and give them all 5, if one likes to cut; or one could reduce the cutting and give out
1 and 2/3 apples. Now imagine that all the apples have gone somewhat bad, and none of your friends care for them. Is there any point in cutting anything? What would dividing by zero accomplish? If you divide by nothing can it be proven that you divided at all?
I imagine that for computers, that something with limited scope could actually simply allow division by zero, by deciding that since the operation can't be accomplished, its a no-op, and is defined as leaving registers and memory unchanged, and perhaps some efficiency could be gained as it would not be necessary to compare to zero and then jump over the division. Another rationale is the division is iterated subtraction as multiplication is iterated addition, and that one can iterate 0 times, by doing nothing. If comp-sci was to make its own rules, I'd say that would be the way to go, as some well designed code, could simpliy factor into straight line code. Of course, this begs the question of whether one could do this with gates or not.
As a young a impressionable uni student doing 1st year maths I once tried to develop a number theory for /0. At the time I reasoned that if someone had done it for -1^1/2 then there probably could be one for /0. Eventually (several pages of scribbled notes) I came up with something similar to what he is suggesting except that I concluded n/0 was a point, not a line, that was outside our frame of reference. So, you bastard, you stole my work. Admittedly I never published anything but... (joke)
Also this doesn't actually solve the problem. It just puts a spin on it. It provides a conceptual way of understanding it.
meh
>in Europe we DO use the dayofmonth/month/year notation... just as a side remark, tough...
I live in the US, and I prefer that order as well. Files sort correctly when you list things that way. But I use '.' characters instead of '/' characters so I won't confuse my fellow Americans who do not write dates in a sortable way.
-------- -------- Support Wesley Clark for president!!!
Well, this seems to simply be another way of saying that Nullity=[b]R[/b]. The difficulty here is that division of two elements in the set of real numbers could produce a set instead of another element of the set. The other way of looking at it is that it produces a variable which is a member of the real numbers, furthermore since the variable can never have a value you could never actually perform any operations on it as you would only get nullity back.
I think this guy is up quack creek.
-------- -------- Support Wesley Clark for president!!!
I don't think this is exactly correct x/0 does not equal infinity. The limit of x/y as y approaches zero is infinity. Infinity is not a number, it just means something is unbounded.
For instance:
a=1
while (true)
a++;
Fell free to trace this program in order to compute your "value" of infinity.
-------- -------- Support Wesley Clark for president!!!
Infinity isn't a number, it's simply means there is an unbounded limit.
-------- -------- Support Wesley Clark for president!!!
Thank you for explaining all of that to me! I had no idea any of this worked, and I've been a professional mathematician for years. You might want to look at the definition of a limit. Which says, (I'm quoting Rudin, but my explanatory additions are in parentheses): Let f be defined on (a set E). Let x be a limit point of E (that is, a point contained in the closure of E). We write f(t) -> A as t -> x, or lim t->x f(t) = A, if there exists a *number* A with the following property: for every epsilon > 0, there exists a delta > 0 such that |f(t) - A| epsilon for all points t of E for which 0|t - x| delta. Using the limit notation for infinite "limits" is an abuse of notation. It's not egregious, and it's useful. But infinity is not a limit, because it isn't even a number.
After all, I am strangely colored.
"If I die and there is an afterlife, I will hunt down the person that made this a convention and make them eat a Null Pill so that their entire body (spirit?) is nullified."
Nulls are like cops, everybody hates them until they need them.
The problem you describe is known as GIGO (Garbage In, Garbage Out). What happens when your example needs to differentiate between "unknown strings" and "empty strings"? Why not do a select that avoids extracting records with NULL's when you don't want them?
Traditionally the "missing data" hassles are pushed all the way from data collection to front end so that the original data (or lack of) is not lost. One rarely knows what a user may want to display in the future and rewritting the front end is simpler than rewriting the whole fucking thing.
And did you exchange a walk on part in the war for a lead role in a cage? - Pink Floyd.
You're talking about the "One Point Compactification" of the Real Line., which produces the "extended Reals". Yes, that works. But 1/x still isn't continuous on that space. For a proof, note that the limit as x->0 from the left is -infinity, but the limit from the right is infinity. A similar question is whether 1/x^2 is continuous at x = 0. I would continue to say no, but the proof I gave above wouldn't work in this case. Even barring using the one point compactification (or just using it implicity), one can give meaning to the use of infinity in limit notation. And they would be pronounced just the same way as regular old limits. Heck, they even (kind of) mean the same thing intuitively. But they are not limits in the strict sense. It's a helpful abuse of notation. Unfortunely, abuses of notation tend to bite mathematicians in the ass when people (like the GGP) think that the meaning and truth of a mathematical statement depends on how it's annotated.
After all, I am strangely colored.
This is a fair summary of what's going on. I would like to point out, however, that in some branches of mathematics (Set Theory, in particular), there are "infinite numbers." Very interesting stuff: See http://en.wikipedia.org/wiki/Ordinal_Number and http://en.wikipedia.org/wiki/Cardinal_Number
:-)
This is neither here nor there in the context of calculus, however. Just thought I'd share.
After all, I am strangely colored.
It just means multiplication is not commutative!
;)
2*(0*infinity) != (2*0)*infinity
"This one goes up to 11".
This Is Spinal Tap
I thought any number divided by zero = infinity
bite my glorious golden ass.
and I thought you cannot be stupid and become a Ph.D. I guess this guy is a counterexample that disproved my conjecture.
So what is nullity - nullity? Does it equal to 0/0 - 0/0 = (0*0-0*0)/(0*0) = 0/0 = nullity? And what does 3*nullity equal to 3*0/0 = 0/0 = nullity? If the answer is yes, this nullity does not interact with other real number at all. And its only purpose being there is to be the answer of 0/0 and 0^0.
Now let me show you how to solve the famous Fermat's Last Theorem problem. Define "dog", "cat", "rabbit" to be the number outside the integers to be the solution of X^n + Y^n = Z^n for some n>2. Then if you want to try, we actually have
dog^n + cat^n = rabbit^n
and n > 2, Yeah!!!! I just solved the Fermat's last theorem, I think I deserve the Fields medal!!!
For those who can understand, real number is not just a set, it is also a additive group and a metric space. Apparently this guy does not even know this.
ha ha he can't use that word. http://en.wikipedia.org/wiki/Null_space
Alright, you've shown you can get to nullity. Now prove to me this, can you get out of nullity?
I was sure when I was doing CS with a Maths major at University that one of my mathematics lecturer claimed that there was already a way to divide by zero using calculus. (Unlike the way we'd been taught in school where we just used very very small values to represent zero). He said he'd show us one day, but he never did.
I'm just wondering if I've missed something in the article. This just seems to be a silly theorem anyway. It doesn't seem to be adding to mathematics to me. I can't think of any use for it that a CS student couldn't have avoided (by having their programs look for divide by zero checks) or anything. Even having a computer accept that a divide by zero becomes a divide by nullity, it doesn't seem to answer anything a computer can use it for. After all, if I have x/0 and the program hits it with x=1223 one time and x=3.556 the next, what sort of answer will the computer throw back if it becomes 1223/nullity or 3.556/nullity. It seems to me that nothing has been answered mathematically and we're not really moving mathematics or computer science any futher ahead in there fields.
Am I missing something? Where does this theorem become practical?
Sure enough, the cow costume was hanging up next to the superhero outfit and sailors uniform. (S,Spud)
I remember this notation only from university physics. As for electric current courses, I don't really remember the way the square root of -1 was written.
Thanks for the reminder
This is a total waste of time. The good doctor's "nullity" works the same way that NaN already does! It gives itself when added to, subtracted from, multiplied by, or used as a quotient, to any number. NaN already does that! NaN is not greater than 0, it is not smaller than 0, it is not equal to 0, NaN is off the number line. There's no need for anyone to go out and start a company. Every existing x87 FPU already works this exact same way.
The only thing he adds is the two values +infinity and -infinity, the positive and negative reciprocals of zero (yes I know that makes little sense). His infinity is not as clean as those of the already-developed hyperreal field, which I believe was already posted about on Slashdot in reference to calculus at some point.
Anyway, at best, this is just another way to sneak an unhandled exception into programs that don't handle certain cases correctly. I have fond memories of one particular piece of instrument control software that, if it encountered a problem during a run (say that a pump went dry, or a high-pressure alert fired), would pop up a modal dialog. Upon dismissal of the modal dialog, the instrument would go back to the main control screen with absolutely no memory of the run it had just finished. No data was left. Undoubtedly some fool had wrapped a try-catch(...) block around the main loop of the program and any random exception like throw highPressureAlert(); would just bubble up all the long, long way to the stop, eating stack frames as it went, undoubtedly leaking memory like a broken sink, all the way up and it's forgotten everything about what it was doing! This is what I would call bad programming.
And that's what happens when you think that you can silently ignore exceptions. Funny things happen. And they can totally disconcert the user and make hash out of everything.
This guy needs a clue. He doesn't seem to know computers or the mathematical literature.
Wikipedia has cataloged a few proposals to fix division by zero:
e r_number_systems
http://en.wikipedia.org/wiki/Division_by_zero#Oth
http://en.wikipedia.org/wiki/Wheel_theory
You can't technically devide by zero, but you can approach it. The closer you get to it the larger the result. You'll never get all the way there, though. In electronics, there's a high and a low. For a car that would be 12V or 0V. If we forget for a moment that math does things the physical world can't, we realize that math is just a tool to help understand the physical world and that some of these laws of math just don't apply to reality. Try to divide by zero and you get the high limit of your system. You're not really dividing by zero, you're dividing by a number that is always approaching but never reaching zero. For an electrical engineer, if you try to divide by zero, you'll end up blowing a circuit breaker because eventually the current will get too high for the wire or power supply to handle. What does infinite current look like? Can you really ever reach 0 ohms? What about zero Kelvins? Are you going to reach that? Zero can't be reached any more than infinity can. You can approach or approximate it, though.
Ops, I shuld have usd the prevuwe but in.
Well, that's about what the Time Cube website says about me. So maybe I need to visit the Flat Earth Society website to be told that too.
-------- -------- Support Wesley Clark for president!!!
so to all the kids out there having trouble with their math assignments:
just introduce a new kind of number and be done with it...
comment first, facts later. http://chem.tufts.edu/AnswersInScience/RelativityofWrong.htm
physics has been dividing by 0 for a long time. It's all in how it's done. Then again, somewhere along the line people started getting confused over the observation/expectation that numbers correctly model the real world. Fortunately, they do to a great extent.
This article was even dumber than I expected it might be. Perhaps the problem is too many dumb-ass'ed coaches being allowed to teach mathematics in public schools.
It's too bad they didn't provide any actual information that this guy actually did something beyond defining o / o as 0 using the classical slash thru the 0 to distinguish between capital o's and a zero. Perhaps if the guy were clever and inventive, the 'nullity' could have been named the 'zoro' which is a little bit closer to this guy's ideal, don qui hote.
It's interesting that Douglas Adams' joke works in both the U.S. and the United Kingdom... In the U.S., people haven't heard the term "zebra crossing", so they assume it's the place in the road where zebras cross, like a deer crossing. In the U.K., "zebra crossing" refers to the black and white bars used to mark a pedestrian crosswalk. Thus, Man gets killed either by a car or a zebra, depending on where you're from.
What? you can't mod up past +5? What kind of arbitrary rule is that?
You don't need provably correct code to avoid a divide by zero.
Whenever you divide, it's not because you're manipulating data structures or hash tables. It's because you've been given a formula or heuristic where division was suggested or required. Only somebody forgot to make sure the divisor can't be zero (surely a sign the original EQUATION or METHOD is wrong, or that input in some other part of the system is being checked for a different valid range).
How many times have you written code where you divided by a non-constant factor determined at runtime? I mean, really? I doubt it's very frequent. All the more reason to be cautious about how you implement said code.
THIS THING CAN TURN ON A DIME, MACROSSZERO STYLE ALSO FUCK BETA, ~NYORON
As if a programmer ever managed to get screwed!
Sexually, that is...
Fundamentalism is a crime against humanity
In terms of analysis (not in terms of computer science), we've been to this brink many times, pondering expressions near division by zero and such. It's why we have the Calculus and Complex Analysis in the first place (thank Leibeniz, Newton, Gauss, Cantor...).
Introducing these terms is like throwing away Calculus and saying: we don't limits and sequences and that notational nonsense, we need absolute, point-in-time answers for every formulation, damn the conseqences.
Of course, this real projective number line lacks the information content carried by similar techniques (Newton's infinitesmals, or other types of transfinite quantites).
It's useless. It really is.
He was just pissed that fields are defined by a set (with no infinities or anything), and two operators (addition and multiplication), and a bunch of axioms. Damn it, he wanted complete closure and wanted all six common arithmetic operators to be onto because it "felt right". So instead we've got an object which is barely a commutative ring (with operators with tons of funky corner cases), and we haven't gained anything in terms of new theorems or strong relation statements from the extra axioms he has to tack on.
I have a feeling that calculus, and measure theory, and all that good stuff has a better handle on infinities than this theory... don't you think?
THIS THING CAN TURN ON A DIME, MACROSSZERO STYLE ALSO FUCK BETA, ~NYORON
(posted Anonymously as I pfafrich modertated this discussion)
I know that many universities place their Computer Science departments within the faculty of Math. Computer science isn't quite the same thing as programming or software engineering, but it definitely illustrates the point.
Regarding the question of software development at least, I'd say the problem is that people trying to make software are dealing with three completely distinct problems at once:
Ultimately, what you end up with is that writing a good piece of software is an engineering task like building a bridge, except that structural engineer has the luxury of hiring comparitively cheap and uniformly skilled construction workers. The software engineer has to hire creative, mathematically-proficient, technically skilled people with a skillset that changes monthly and varies wildly from person to person. And who ideally understand enough of the engineering to deal with all of the planning and verification thingies that need to be done.
That's my perspective anyway, from my brief time in the industry...
There are some very interesting things about zero, and triviality. First, "The Existence of a Trivial is Indeterminate". This is very important and easy to prove. It says that you cannot prove whether an object is really itself, or if it might in fact be an identical clone of itself. That this is strictly "indeterminate". This is also true of numbers, etc. This is Harris's Theorem, and is perhaps the most important theorem in all of mathematics. I'm not sure if his "nullity" is the same as triviality, but it might be. I am not familiar with what this man is doing. Next, when are apples equal to oranges ? When you have zero of them !! Yes - indeed - zero apples is identical to zero oranges. There is no difference !! Triviality is not a trashcan. There is a distinction between the trivial and the strictly nonexistent. If this man is teaching nonsense to schoolchildren then he should be flogged. But if he is investigating the idea of triviality then I'd say he should get a medal. I think that I'd need to see his math first before making that call. Is an apple the same as an orange ? Yes, when you have 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 ! You have existence, nonexistence, and there IS a third existential type which is the trivial. It is a third type because "The Existence of a Trivial is Indeterminate", and I can prove it easily. All you need to do is play with uniqueness. http://sciphysicsopenmanuscript.blogspot.com/ Respectfully, Dr. Viktor I. Planckenstein
"The Existence of a Trivial is Indeterminate". This is very important and easy to prove. It says that you cannot prove whether an object is really itself, or if it might in fact be an identical clone of itself. That this is strictly "indeterminate". This is also true of numbers, etc. This is Harris's Theorem, and is perhaps the most important theorem in all of mathematics. I'm not sure if his "nullity" is the same as triviality, but it might be. I am not familiar with what this man is doing. Triviality is not a trashcan. There is a distinction between the trivial and the strictly nonexistent. You have existence, nonexistence, and there IS a third existential type which is the trivial. It is a third type because "The Existence of a Trivial is Indeterminate", and I can prove it easily. All you need to do is play with uniqueness. http://sciphysicsopenmanuscript.blogspot.com/ [blogspot.com] Respectfully, Dr. Viktor I. Planckenstein
Pi is definitely a well-defined real, and so is e!
Real are constructed by taking bracketed infinite sets of increasing and decreasing fractions (Q) that converge on the real.
So pi is defined as the the pair of:
[largest in the set of fractions definitely less than pi, smallest in the set of fractions definitely greater than pi]
Think of the inner and outer circumscribed polygons closing in on a circle. (The formulas with the delta/epsilon bits evade me, but they definitely exist)
And a classic example, the real number 1 is [0.99999999... (sum(9/10^n)), 1.0000000... (1+1/10^n)]
But infinity can't be bracketed. (What fraction is trivially larger than a fraction trivially smaller than "infinity", when you can't even use infinity in the definition for the fraction expansion?)
You have to prove some expansion, that by mathematical induction, as n increases, the different between the least upper and most lower bounds decreases monotonically. You'll find you can't create a suitable expression defined in terms of Q to place in the left and right sides. (There is a proof of this, but I'm not familiar with it).
Which leads to R not having infinity as a set member.
THIS THING CAN TURN ON A DIME, MACROSSZERO STYLE ALSO FUCK BETA, ~NYORON
How much nothing can you fit in nothing?
That is not what he is proposing. His proposition is that we link negative and positive infinity, like bending a wire into a ring and soldering it together. Then, just as you can easily refer to the point on the ring called "0", you can now also easily refer to the point on the "opposite side" of the ring, the "+/- infinity" aka "nullity" point.
There are many models where this representation could potentially be more convenient than others we have used before.
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