Re: __builtin_cpow((0,0),(0,0))

[Joe Buck <Joe dot Buck at synopsys dot COM>]

On Tue, Mar 08, 2005 at 01:47:13AM +0100, Ronny Peine wrote:
> Hi again,
> 
> a small proof.
> 
> if A and X are real numbers and A>0 then
> 
> A^X := exp(X*ln(A)) (Definition in analytical mathematics).

That is an incomplete definition, as 0^X is well-defined.

> 0^0 = lim A->0, A>0 (exp(0*ln(A)) = 1 if exp(X*ln(A)) is continual continued

Your proof is wrong; since you even propose it you probably have not been
exposed to partial differential equations.  You have a two-dimensional
plane; you can approach the origin from any direction.

The direction you chose was to keep the exponent constant at 0.  Then
you get a limit of 1.

An alternate choice is to keep the base constant at 0, choose a positive
exponent and let it approach zero.  Then you get a limit of 0.