Re: Re: Re: What is zero divided by zero?

*To*: mathgroup at smc.vnet.net*Subject*: [mg48600] Re: [mg48585] Re: [mg48563] Re: What is zero divided by zero?*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Mon, 7 Jun 2004 05:33:26 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*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>*Reply-to*: murray at math.umass.edu*Sender*: owner-wri-mathgroup at wolfram.com

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

**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>