On Sun, 11 Mar 2007, Jay Belanger wrote:
> In what way is 0^0 ambiguous, and are there any cases where 0^0=1 is
> wrong?
Of course, yes:
lim 0^x = 0 (x -> +0)
More generally,
lim x^y
does not exist when both x and y tend to 0 (and are positive). The limit
depends on the path along which (x,y) approaches (0,0). By choosing an
appropriate path, one can easily obtain any non-negative value for this
limit.
Andrey