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Re: What is zero divided by zero?

• To: mathgroup at smc.vnet.net
• Subject: [mg48563] Re: What is zero divided by zero?
• From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
• Date: Sat, 5 Jun 2004 07:19:06 -0400 (EDT)
• References: <4xm5ym42r3vg@legacy> <wzog6i63na4c@legacy> <c9k4bo$fi9$1@smc.vnet.net> <c9pfb1$s4l$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

drbob at bigfoot.com (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,
> undefined.

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

• Follow-Ups:
  • Re: Re: What is zero divided by zero?
    • From: Murray Eisenberg <murray@math.umass.edu>
  • Re: Re: What is zero divided by zero?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>