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Re:Why can't we divide by zero? by derefr on Sunday September 28, 2008 @07:42PM (#317916)
Is it at least true that (0 < |0/0| < Infinity); that is, that 0/0 is a finite, non-zero number?
Re:Why can't we divide by zero? by newt0311 on Sunday September 28, 2008 @07:58PM (#317928)
No. 0/0 is completely undefined. For example, consider limit as x approaches 0 of (-x)/x. This approaches (-0)/0 = 0/0 but simplifying the limit given an answer of -1. So 0/0 is completely dependent on the characteristics of the convergence and had no meaning in isolation. In fact, the field of real (and complex) numbers does not even include 0 in the multiplicative group. Therefore, dividing by 0 is nonsensical as it has no inverse as it is not in the multiplicative field. According to the basic axioms of groups theory, given a field F with a the identity of the additive group in the field and b some element of the multiplicative group, it can be proven that mul(a,b) = a where mul is the multiplication operation. This explains why 0 times any other number is 0. If you would like a copy of the proof, just drop me an email.

Sorry for the rant, math major.

Re:Why can't we divide by zero? by cheese825 on Monday September 29, 2008 @12:15AM (#318092)
I'd love to see the proof. But you did not post your email address. Could you send it to mine?
Re:Why can't we divide by zero? by newt0311 on Monday September 29, 2008 @04:11AM (#318202)
oops. Sorry about that. Fixed.

PS. Your email address is not posted either.

Re:Why can't we divide by zero? by hhm on Monday September 29, 2008 @09:45AM (#318324)
Isn't it something like this?

0=a-a, for all a

(where a-a is actually, a+(-a))

so: mul(b,0)=mul(b,(a-a))=mul(b,a)-mul(b,a)=z-z=0

Re:Why can't we divide by zero? by newt0311 on Monday September 29, 2008 @10:04AM (#318343)
pretty much.