From: Mathieu Bouchard <matju@...>
Date: 2005-03-20T09:47:46+09:00
Subject: Re: 0**0==1?


On Sat, 19 Mar 2005, Christian Neukirchen wrote:

> Bertram Scharpf <lists@bertram-scharpf.de> writes:
> > this is difficult to feed Google with:
> >>> 0**0
> > => 1
> >>> 0**0.0
> > => 1.0
> >>> 0.0**0
> > => 1.0
> >>> 0.0**0.0
> > => 1.0
> > Shouldn't the result be a NaN?
> Interesting... Perl and Python say 0**0 is 1, Maxima (that should know
> better) says 0 but generates an error...
> To quote http://mathworld.wolfram.com/ExponentLaws.html:
> > The definition 0**0=1 is sometimes used to simplify formulas, but it
> > should be kept in mind that this equality is a definition and not a
> > fundamental mathematical truth (Knuth 1992; Knuth 1997, p. 56).

It's true that 0**0 is undefined, but I think 0**0 should give 1 because
it is common for polynomials to be defined with the constant term being
x**0. It wouldn't be nice if this didn't work. There are also cases where
0**0 could be defined otherwise contextually, such as with a value of 0,
but they are rare.

_____________________________________________________________________
Mathieu Bouchard -=- Montr�al QC Canada -=- http://artengine.ca/matju