Re: What is zero divided by zero?

• To: mathgroup at smc.vnet.net
• Subject: [mg48652] Re: What is zero divided by zero?
• From: drbob at bigfoot.com (Bobby R. Treat)
• Date: Wed, 9 Jun 2004 04:17:27 -0400 (EDT)
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• Sender: owner-wri-mathgroup at wolfram.com

```And yet again, it remains undefined. Let's leave it that way.

Bobby

Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote in message news:<ca3hin\$s0f\$1 at smc.vnet.net>...
> > That it might be useful to form this "field", under some name, allow
> > the multiplicative identiy to equal the additive identity, and thereby
> > to see that 0^(-1) = 0, so that 0/0 = 0 in this "field", still doesn't
> > provide a compelling argument to ME for saying 0/0 = 0 in other
> > contexts!
>
> But then nobody ever said that. In fact it was obvioulsy a joke, though
> I guess it needs a certain kind of sense of humour to appreciate it. As
> for Zen ,  well  ... never mind.
>
> Andrzej
>
>
>
>
>
> On 8 Jun 2004, at 01:19, Murray Eisenberg wrote:
>
> > Names have great stipulative and connotative power.
> >
> > Ceratinly the meanings of math names gets extended all the time, but
> > one can ask whether breaking certain constraints on use of a name
> > would, for purposes of communication and understanding, best result in
> > a new name -- or at least clear warning to the reader that an
> > unvonventional use of the term is being used.
> >
> > With your intended broadening of the term, one would of course
> > immediately ask which established theorems about finite fields have to
> > be restated (if any), which definitions relaxed, etc.
> >
> > That it might be useful to form this "field", under some name, allow
> > the multiplicative identiy to equal the additive identity, and thereby
> > to see that 0^(-1) = 0, so that 0/0 = 0 in this "field", still doesn't
> > provide a compelling argument to ME for saying 0/0 = 0 in other
> > contexts!
> >
> >
> > Andrzej Kozlowski wrote:
> >
> >> I find your argument strange. I am a mathematician and I have
> >> published papers where I have introduced new definitons and new
> >> terminology, as has practically every research mathematician. I am
> >> free to introduce any new concept and name it anyway I like (though
> >> of course I can't force others to use my terminology) if it is
> >> self-consistent, useful and I make my meaning clear. The fact that
> >> "folks don't ordinarily speak of it" is relevant only until sombody
> >> chooses to do otherwise.
> >> The set with one element with the obvious operations of addition and
> >> multiplication satisfies all the axioms of a field except the
> >> convention that 1 should be different form 0. It is perfectly well
> >> defined, it is useful for the purpose of this thread, and 1/0 =1 = 0
> >> holds in it. I chose to call it a "field" though I could equally well
> >> have called it a "desert"  but how does the name change anything?
> >> Andrzej
> >> On 7 Jun 2004, at 18:33, Murray Eisenberg wrote:
> >>> I'm not sure what Zen world you refer to, but so far as I have met
> >>> the
> >>> term "field" in the actual mathematical world, the smallest field
> >>> has 2
> >>> elements, not 1.
> >>>
> >>> Thus, from http://mathworld.wolfram.com/Field.html:
> >>>
> >>> "Because the identity condition must be different for addition and
> >>> multiplication, every field must have at least two elements."
> >>>
> >>> (I suppose you could say that, in the trivial ring consisting of just
> >>> the 0 element, 0 is its own multiplicative inverse, since 0 * 0 = 0
> >>> and
> >>> 0 is a multiplicative identity.  But folks don't ordinarily speak of
> >>> multiplicative inverses, and hence don't speak of quotients, unless
> >>> there's a multiplicative identity 1 =/= 0.)
> >>>
> >>>
> >>> Andrzej Kozlowski wrote:
> >>>
> >>>> 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
> >
> >
> > --
> > Murray Eisenberg                     murray at math.umass.edu
> > 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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