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MathGroup Archive 2004

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Re: Re: What is zero divided by zero?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48585] Re: [mg48563] Re: What is zero divided by zero?
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sat, 5 Jun 2004 19:58:06 -0400 (EDT)
  • References: <4xm5ym42r3vg@legacy> <wzog6i63na4c@legacy> <c9k4bo$fi9$1@smc.vnet.net> <c9pfb1$s4l$1@smc.vnet.net> <200406051119.HAA11743@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 5 Jun 2004, at 20:19, David W. Cantrell wrote:

> 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
>
>

There is at least one mathematical context where it is perfectly well 
defined: the Zen-like world of the field with one element, where
0/0 = 0 = 1.
Andrzej



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