In article <XnsA26BE4E8ADCECgoddardbenetscapenet@22.214.171.124>, Bart Goddard <email@example.com> wrote:
> Dan Christensen <Dan_Christensen@sympatico.ca> wrote in > news:firstname.lastname@example.org: > > > > 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. --