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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 12:10 AM

On Friday, October 4, 2013 6:37:17 PM UTC-4, graham...@gmail.com wrote:

>
> That you pick the point x=0 and deliberately give it different values
>
> and making oo many superfluous functions in place of an unknown
>
> to support your view 0^0 is not 1 is rather obscure.
>

Not just any functions, but functions that agree everywhere but at (0,0). Make a table of values and verify for yourself that changing the value of 0^0 has no effect on the other entries if you use these defining equations:

(1) x^0 = 1 for x=/=0
(2) x^(y+z) = x^y * x

>
>
> Plot every point of X^Z on a 3D graph and 0^0 is clearly 1.
>

I really wish that was true, but it seems our high school teachers had it right all along.

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