long time reader, first time writer...
On Tue, Oct 15, 2002 at 10:06:37PM +0200, Angel Faus wrote: > > > > > Mathematically, 1/0 is whatever you define it to be. > > > > Well, sure. That's as axiomatic as saying, "mathematically, the > > number one is whatever you define it to be." But a mathematical > > system that has a definition which is inconsistent with the rest of > > the system is a flawed one. If you let 1/0 be *anything*, then > > ordinary algebraic logic falls apart. Those silly proofs where it > > is "proven" that 1 = 2, 1 + 1 = 1, etc., all depend on division by > > zero being possible (regardless of what its value is). You have to > > keep division by zero illegal to avoid these absurd results. > > Hence, to my mind at least, exception-throwing or NaN is a better > > solution than infinity. > > > > My point was that there is no stone-carved mandate of the ancient > mathematicians saying whether the value of 1 / 0 is defined or not. I > did not intend to say that you could assign it any value. Well, yes and no. The original progenitor of the number zero did say that he thought 0 / 0 should be 0, so mathematicians haven't always gotten it right. But it can be proven that 1 / 0 should be undefined, and once it's been proven, it doesn't need to be gone over again -- effectively setting it in stone. So for instance, 1 / 0 is not defined because the division algorithm explicitly fails to work correctly for it[1]. If you can't use the division algorithm how do you expect to divide? It cannot be done. 1 / 0 can only be construed as +Inf if we're discussing limits of functions such that the denominator approaches 0 (from the positive side). It does not appear that we are discussing such things, but the actual integers 1 and 0. Even in the case of limits i am want to be careful, for infinity is not technically a number, but a convenient concept used to describe certain behaviors... > It is general practice among mathematicians to say that is undefined, > but it is also general practice among other respectable ocupations to > say it is "something like infinite", and both approaches can be > formalized. No offense, but i would love to see someone's formalization that the integer division 1 / 0 is equivalent to infinity. Mostly because i would attempt to rip it asunder :) (i might fail, but i would try...) > My personal opinion is that a language that lets you add "apples" + > "oranges" and get 0, shouldn't be too picky about 1 / 0 not being a > "proper" number. i more have to agree with tilly on this one[2]. Essentially, if i ever divide by zero, it's probably an unmistakable error on my part. And it should raise a trappable error so that if i'm expecting it i can shuffle it under the rug, and if i'm not i'll be notified that something went 'splody. jynx [1]: This comes from a recent discussion on perlmonks where i attempted to formally iron things out for people, since i have yet to see anywhere thus far on the web where it was actually formalized. (formalization being markedly different from rationalization) http://www.perlmonks.org/index.pl?node_id=203698 [2]: Tilly's opinion can be found at the following: http://www.perlmonks.org/index.pl?node_id=98996 +-------------------------------------+ |jynx d mouse | |[EMAIL PROTECTED] | |"You're just another X" --Filter| +-------------------------------------+
