Re: [Axiom-developer] Complex exponentiation and 0

[Bertfried Fauser]

On Mon, 21 Jun 2004, Martin Rubey wrote:

Hi,

from a math point of view, 0^0 is introduced to cope with patological
examples in the standard terminology (this allows to fomulate definitions
and theorems without saying if x>0 then ... else ....)

>From an algebraic point of view, I think its save to assume 0^0=1 in any
category which has _no_ (non-discrete) topological semantics. As eg. real
numbers come with a standard topology, 0^0 is not a uniquely definalble
object.

Hence as a guidline, every object with allows a "limit" (ie some norm
established) should _not_ assume that 0^0=1. I don't see problems for say
natural numbers.

ciao
BF.

% PD Dr Bertfried Fauser
%     Institution: Max Planck Institut for Math, Leipzig <http://www.mis.mpg.de>
%   Privat Docent: University of Konstanz, Phys Dept 
<http://www.uni-konstanz.de>
%  contact|->URL : http://clifford.physik.uni-konstanz.de/~fauser/
%          Phone : Leipzig +49 341 9959 735  Konstanz +49 7531 693491