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MathGroup Archive 2004

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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
>
>


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