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Re: Re: What is zero divided by zero?

  • To: mathgroup at
  • Subject: [mg48591] Re: [mg48563] Re: What is zero divided by zero?
  • From: Murray Eisenberg <murray at>
  • Date: Sat, 5 Jun 2004 19:58:13 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <4xm5ym42r3vg@legacy> <wzog6i63na4c@legacy> <c9k4bo$fi9$> <c9pfb1$s4l$> <>
  • Reply-to: murray at
  • Sender: owner-wri-mathgroup at

A really reasonable thing is to let the user decide what to do about the 
value of such troublesome expressions.  One can do this in Mathematica.

(I once proposed making such a user setting available in APL. There's no 
comparable facility in J.)

David W. Cantrell wrote:

> drbob at (Bobby R. Treat) wrote:
>>"zero divided by zero" is four English words, one after the other. The
>>meaning of it is whatever we can agree that it means. But we can't
>>agree on a useful meaning; it's not as if the subject hasn't come up a
>>million times over the past century or two. It is, and will remain,
> Well, it is normally regarded as being undefined in mathematics _per se_,
> yes. But it certainly is defined in some contexts related to computing.
> Examples:
> In APL, it's 1 (which, IMO, is quite regrettable),
> while in APL's offspring J, it's 0 (which is the only reasonable choice
> among the reals).
> And it's defined in standard floating-point arithmetic to be NaN. (Now
> you're welcomed to say "But that's merely defining it to be 'undefined'!"
> Although that's right in some sense, in fact it is nonetheless _defined as
> a specific floating-point object_, and that can be useful.)
> David Cantrell

Murray Eisenberg                     murray at
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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