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

[Paul Schlie <schlie at comcast dot net>]

> Gabriel Dos Reis wrote:
> You probably noticed that in the polynomial expansion, you are using
> an integer power -- which everybody agrees on yield 1 at the limit.
>
> I'm tlaking about 0^0, when you look at the limit of function x^y

Out of curiosity, on what basis can one conclude:

 lim{|x|==|y|->0} x^y :: lim{|x|==|y|->0} (exp (* x (log y))) != 1 ?

As although it's logarithmic decomposition may yield intermediate complex
values, and may diverge prior to converging as they approach their limit,
it seems fairly obvious that the expression converges to the value of 1
about the limit of 0; as although it may be argued that the (log 0) is
undefined (it more accurately -> -inf), but does so at an exponentially
slower rate than it's operand, i.e.: lim{|x|==|y|->0} (* x (log y)) = 0,
thereby lim{|x|==|y|->0} (exp (* x (log y))) = (exp 0) = 1; it would seem?