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MathGroup Archive 2004

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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)
  • References: <4xm5ym42r3vg@legacy> <wzog6i63na4c@legacy> <c9k4bo$fi9$1@smc.vnet.net> <c9pfb1$s4l$1@smc.vnet.net> <200406051119.HAA11743@smc.vnet.net> <200406052358.TAA28968@smc.vnet.net> <200406070933.FAA10935@smc.vnet.net> <6190E72C-B898-11D8-B3A8-000A95B4967A@mimuw.edu.pl> <40C495AE.2060607@math.umass.edu> <ca3hin$s0f$1@smc.vnet.net>
  • 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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