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.
