-----maxima-bounces at math.utexas.edu wrote: -----
>Oh, and by the way, here's Knuth et al ("Concrete Mathematics") on 0^0:
>
>
>"Some textbooks leave the quantity 0^0 undefined, because the
> functions x^0 and 0^x have different limiting values when x
> decreases to 0. But this is a mistake. We must define x^0=1 for all
x,
> if the binomial theorem is to be valid when x=0, y=0, and/or x=-y.
> The theorem is too important to be arbitrarily restricted! By
> contrast, the function 0^x is quite unimportant."
>
Mostly off topic: I like "Concrete Mathematics" a great deal, but this
reasoning is just plain hokie. All this would be better expressed
by something like: If we don't agree that 0^0 = 1, we would need to peel
the
first term off from most the summations in this text. That would be ugly.
Instead, let's agree that 0^0 = 1. In other contexts, the definition 0^0 =
1
might not be a good thing.
Barton