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Re: Zero divided by a number...

  • To: mathgroup at
  • Subject: [mg51789] Re: Zero divided by a number...
  • From: "David W. Cantrell" <DWCantrell at>
  • Date: Tue, 2 Nov 2004 02:05:11 -0500 (EST)
  • References: <dz50uwrnio0u@legacy> <cm4qoc$6j6$>
  • Sender: owner-wri-mathgroup at

rwprogrammer at (Richard) wrote:
> 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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