__builtin_cpow((0,0),(0,0))

[Ronny Peine]

Joe Buck wrote:
> 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.
> 

Well, then it would be lim x->0 (0^x) = 1 because 0^x is 1 for every x 
element of |R_>0