On 12 May, 15:21, Mark Dickinson <[EMAIL PROTECTED]> wrote: > On May 12, 2:09 am, "Terry Reedy" <[EMAIL PROTECTED]> wrote: > > > Then it seems equally dubious that 0.**y, y>0, should be well-defined. > > It seems to me that lim as x goes to 0. exp(y*log(x)) is equally well > > defined whether y is 0 or not, even though there is a discontinuity in the > > limit. > > Well, there's a difference: the limit of exp(y*log(x)) as (x, y) -> > (0, a) exists for all finite nonzero a. The limit as (x, y) -> > (0, 0) doesn't.
But exp(y*log(x)) -> 1 as (x, y) -> (0, 0) along any analytic curve which is not the x=0 axis (I think at least - it seems easy to prove that given f and g analytic over R, f(x)*ln g(x) -> 0 as x -> 0 if f(0)=g(0)=0 and g(x)>0 in the neighbourhood of 0). This should cover most practical uses? -- Arnaud -- http://mail.python.org/mailman/listinfo/python-list
