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Topic: An Infinity of Exponent-like Functions on N
Replies: 31   Last Post: Oct 23, 2013 10:48 AM

 Messages: [ Previous | Next ]
 Dan Christensen Posts: 8,219 Registered: 7/9/08
Re: An Infinity of Exponent-like Functions on N
Posted: Oct 5, 2013 12:19 AM

On Friday, October 4, 2013 7:45:20 PM UTC-4, fom wrote:

>
> Consider the phrase:
>
>
>
> "Notwithstanding combinatorial analogies and
>
> arguments of convenience..."
>
>
>
> You have not *proven* that your criticism is
>
> not an "argument of convenience".
>
>
>
> The burden of proof has been "conveniently"
>
> placed upon all contrary opinions.

The fact is, like 0/0, any value with work for 0^0. If you also want to assume that x^(y+z) = x^y * x^z for all x,y,z in N, then you could narrow it down to either 0 or 1. As far as I know, there is no compelling logical reason to choose any one particular value. IMHO, none have been presented here.

Dan

Date Subject Author
10/4/13 Dan Christensen
10/4/13 Graham Cooper
10/4/13 fom
10/4/13 Graham Cooper
10/5/13 Dan Christensen
10/5/13 Peter Percival
10/5/13 fom
10/5/13 Dan Christensen
10/5/13 Graham Cooper
10/5/13 fom
10/5/13 Dan Christensen
10/5/13 fom
10/5/13 Dan Christensen
10/5/13 Graham Cooper
10/5/13 Dan Christensen
10/5/13 Peter Percival
10/5/13 Graham Cooper
10/6/13 Peter Percival
10/5/13 Peter Percival
10/5/13 Dan Christensen
10/10/13 Shmuel (Seymour J.) Metz
10/10/13 fom
10/10/13 Peter Percival
10/23/13 Shmuel (Seymour J.) Metz
10/23/13 Michael F. Stemper
10/10/13 Michael F. Stemper
10/5/13 Dan Christensen
10/6/13 Dan Christensen
10/6/13 Brian Q. Hutchings
10/6/13 Dan Christensen
10/5/13 William Elliot
10/5/13 Peter Percival