The problem with Zero

[{P²P}Apocalypse]

Sorry I could'nt find the link and forgot to bookmark it. But, this question came up and was posted recently. So I asked my dad who has a PHD in mathamatics and teaches physics. I asked him what the current take on zero is in the math world as pertaining to this particular problem. So here is the original question and his answear to the problem.

> An interesting mathematical dilemma:
>
> 0/0=?
>
> Three absolutes (as I was taught):
>
> Anything divided by zero is undefined
> Zero divided by anything is zero
> Anything divided by itself is one
>
> What is your opinion on this? (give reasons)


Division is defined in terms of multiplication which is an "assumed" operation unless you are studying set theory where number, addition, and multiplication are defined.

For any three real numbers, a/b = c if and only if bc = a. For example 8/2 = 4 because 2(4) = 8 , in other words, it checks.
Now suppose a = 8 and b = 0 and suppose that 8/0 = c where c is some real number. Then 0(c) = 8 since it must check. However, 0(any real number ) = 0. Now both properties cannot be true. Either we can't have an answer to any non-zero number divided by zero or we can have the property that 0 times any number is zero. Mathematicians faced this choice years ago and decided that 0 times any number equals zero is the more valuable property in the real number system. Consequently, division on a non zero number by 0 is not defined.

What about 0/0? Suppose we say 0/0 = c where c is some real number. Will it check? 0(c) =0. Certainly it checks. What value should we give c? Why not 1? 0/0=1 since 0(1) = 0. But 52 would work equally well. 0/0 = 52 since 0(52) = 0. Since any number will check, 0/0 lacks a "unique" answer. Again mathematicians ruled out 0/0 as a permissible operation because of this lack of uniqueness.

There are some weird number systems where division by the zero of the system is permissible. Those systems have some rather strange properties that renders them nearly useless in solving problems in the real world which is the primary purpose of mathematics.

[cwk9]

ow! my head.

[Tim_axe]

It makes sense reading it now...

I guess the real-world applicibility of math shows, even with 0/0... Nothing for nobody means Something for anybody, because of the double negatives. The opposite of nobody isn't one specific thing, so 0/0 (nothing for nobody) can equal anything (anybody), and I guess that it conforms to the real-world... This is a much better explanation of what I had been thinking... Great job {P²P}Apocalypse! My mind is confused no more!


-Tim_axe

[ams2d]

Great post Apocalypse. Explained clearly for such a confusing concept.

Which systems allow 0/0?

[JRoc]

Holy **** man.... what grade ya in? Thats like hard as hell and now, not only do I feel dumb but my head hurts like ****ing hell.

[souleman]

But then if you get into calc, you could probably answer that question, because you can use sets of numbers, so it would be the set of all numbers from -infinity to +infinity.....

That would make more sence if I knew how to use mathmatical functions in this little reply box...

[Vorlin]

And people think programming is hard... hehe... I think I'll go let my nose stop bleeding now.

[SarinMage]

0 is all sorts of ****ed up cause it represents something that doesent exist, and represents the middle of everything (.........-2,-1,0,1,2,.....)

kinda does, if you get what i mean,

[11001001]

Originally said by Ralph Wiggum on The Simpsons
My Brain Hurts.

[Kezil]

Thanks for the reply to my question, the clearest I've seen yet.
Here's the link to the original question: http://www.antionline.com/showthread...hreadid=226505
And to another related question: http://www.antionline.com/showthread...hreadid=131747

I love math, and constantly look for new things about it (and science) to learn. Unfortunately (oddly enough) school doesn't give me enough time to pursue my interest in it as far as I like. So now, I'd like to ask any who read this to post anything interesting in math you can (sorry that this is in a security forum, but it does relate to programming and cryptography).

Thank you