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Re: [Axiom-developer] Complex exponentiation and 0
From: |
Bertfried Fauser |
Subject: |
Re: [Axiom-developer] Complex exponentiation and 0 |
Date: |
Mon, 21 Jun 2004 12:53:25 +0200 (CEST) |
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>
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