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 > >

**Follow-Ups**:**[Off Topic] Re: Re: What is zero divided by zero?***From:*János <janos.lobb@yale.edu>

**References**:**Re: What is zero divided by zero?***From:*"David W. Cantrell" <DWCantrell@sigmaxi.org>

**Re: Re: What is zero divided by zero?***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**Re: Re: Re: What is zero divided by zero?***From:*Murray Eisenberg <murray@math.umass.edu>

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