Re: Re: Zero divided by a number...

*To*: mathgroup at smc.vnet.net*Subject*: [mg51926] Re: [mg51897] Re: Zero divided by a number...*From*: DrBob <drbob at bigfoot.com>*Date*: Fri, 5 Nov 2004 02:17:21 -0500 (EST)*References*: <cm9ut5$8ii$1@smc.vnet.net> <200411040650.BAA18169@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

On the one hand, I claim ComplexInfinity is a subspecies of "undefined". If not, on the other hand, then Mathematica improperly "defines" 1/0, which really should be undefined. Bobby On Thu, 4 Nov 2004 01:50:55 -0500 (EST), David W. Cantrell <DWCantrell at sigmaxi.org> wrote: > Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote: >> Everything Richard wrote is correct. He only forgot to say that that >> all these statements are true as statements about *complex numbers*. >> Thus instead of saying "x/0 is undefined ..." he should have said "is >> undefined as a complex number" or "is not a complex number" etc. The >> word "number" is ambiguous, and there are some strange people, even >> some mathematicians, who call things like Infinity "numbers" but I have >> never heard of anyone refer to them as "complex numbers'. > > Perhaps you would be amused to know that Bertrand Russell, in constructing > what we might nowadays call the positive extended reals from the positive > rationals, refers to "the real number infinity". But that is merely of > historical interest. The real and complex number systems, as we know them > today, contain no infinite elements, of course. > >> ("Complex" of course includes "real"). >> (Besides, I don't believe that there is anyone, including yourself, who >> really did not understand what Richard meant.) > > I thought and I still think that I understood exactly what Richard meant. > > Not only is this a _Mathematica_ newsgroup, but Richard himself _supplied > context_. He said "Mathematica handles 0 appropriately. x/0 is undefined > for any number x." So it seems clear to me that he thought, incorrectly, > that _in Mathematica_ x/0 is always undefined. > > Indeed, I would not be at all surprised if Richard -- after realizing that > 1/0 is ComplexInfinity, rather than undefined, in Mathematica -- now thinks > that Mathematica does _not_ handle division by 0 appropriately. > > David Cantrell > > >> On 2 Nov 2004, at 16:05, David W. Cantrell wrote: >> > >> > rwprogrammer at hotmail.com (Richard) wrote: >> > [snip] >> >> Mathematica handles 0 appropriately. x/0 is undefined for any number >> >> x. >> > >> > In Mathematica, it is _not_ true that "x/0 is undefined for any number >> > x." Rather, for any nonzero x, x/0 is defined as ComplexInfinity. >> > >> >> This is extremely simple to see if only you view division as the >> >> opposite of multipication. >> > >> > That view of division is simply inadequate in number systems (such as >> > the extended complex numbers) in which division of nonzero quantities >> > by zero is defined. >> > >> >> A/B = C implies that C * B = A. >> >> >> >> 12/4 = 3 because 3*4 = 12. >> >> 0/7 = 0 because 0*7 = 0. >> >> 7/0 is undefined because x*0 does not equal 7 for any number x. >> >> Therefore it has no answer (except undefined). >> > >> > In Mathematica, 7/0 yields ComplexInfinity, but that certainly does not >> > imply that 0 * ComplexInfinity = 7. (In fact, 0 * ComplexInfinity is >> > Indeterminate in Mathematica.) > > > > -- DrBob at bigfoot.com www.eclecticdreams.net

**References**:**Re: Zero divided by a number...***From:*"David W. Cantrell" <DWCantrell@sigmaxi.org>