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
