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: <email@example.com> <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.
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
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