Newsgroups: sci.math
From: hoey@aic.nrl.navy.mil (Dan Hoey)
Date: 05 Mar 1995 21:47:47 GMT
Subject: Re: 0^0 should equal 1. Right???

mdek...@fwi.uva.nl (Martijn Dekker) writes:

> d...@kaa.informatik.rwth-aachen.de (David Kastrup) wrote:

> :... An empty product, however, is 1,
> :like an empty sum is 0. Everything else does not make sense.

> no, an empty product is not equal to 1, it is in some cases
> *defined* as 1 for convenience. same for ths empty sum being 0.

Your distinction is vacuous.  It is "convenient" in any ring with an
identity, as are all the systems we are discussing here.  And so it
is defined to be 1 "for convenience" just as conveniently as 1+1 is
defined to be 2.  It is ridiculous to try to make 0^0 to be less
identical to 1 than 2-1.

Dan
Hoey@AIC.NRL.Navy.Mil