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

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

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