Date: Nov 2, 2013 12:16 AM
Author: Virgil
Subject: Re: Formal proof of the ambiguity of 0^0

In article <XnsA26BE4E8ADCECgoddardbenetscapenet@74.209.136.90>,
Bart Goddard <goddardbe@netscape.net> wrote:

> Dan Christensen <Dan_Christensen@sympatico.ca> wrote in
> news:63ae3975-e4f7-4381-9df0-4957c8b0f5e9@googlegroups.com:
>
>

> > As I have said repeatedly, it is assumed to be a natural number, but
> > no specific value is assigned to it. So, yes, that makes it
> > "undefined." What is your point, Barty?

>
> The point, as I've said repeatedly, is that your
> "theorem" assumes that it has a value. If it's not
> defined, then it has no value (or meaning.) Contradiction.
> 0^1 is defined in terms of 0^0. So now, 0^1 is
> undefined.


I believe that x^1 can be defined as x for all real x,
without requiring any definition for x^0 at all,
and then x^2 can be defined as (x^1)*x for all real x.
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