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

*To*: mathgroup at smc.vnet.net*Subject*: [mg51820] Re: [mg51789] Re: Zero divided by a number...*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Wed, 3 Nov 2004 01:23:41 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

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'. ("Complex" of course includes "real"). (Besides, I don't believe that there is anyone, including yourself, who really did not understand what Richard meant.) Andrzej Kozlowski Andrzej Kozlowski Chiba, Japan http://www.akikoz.net/~andrzej/ http://www.mimuw.edu.pl/~akoz/ 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.) > > David Cantrell > >