In article <[EMAIL PROTECTED]>, "Terry Reedy" <[EMAIL PROTECTED]> wrote:
> "Mark Dickinson" <[EMAIL PROTECTED]> wrote in message > news:[EMAIL PROTECTED] > On May 11, 9:36 pm, "Terry Reedy" <[EMAIL PROTECTED]> wrote: > |> Do you have in mind any situations in which it is advantageous to have > 0**0 > |> undefined? > > | (Playing devil's advocate here.) If you regard x**y as exp(y*log(x)) > > Which, of course, I was not, but for the sake of discussion.... > > | then it's not at all clear that 0.**0. should be considered well-defined. > > 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. Huh? That "discontinuity" is the problem. Actually, the problem is that the function f(x,y)=x**y=exp(y*ln(x)) will be double valued at x=0 and y=0. It's value will depend on the direction in which the limit approaches (x,y)=(0,0). You cannot have a function that has two values at one domain point without adding branch cuts (see complex functions like ln(z), z is complex). That's not well defined -- in your sense. You are choosing a branch cut and you must make sure the rest of your math and code are consistent with that. You should also tell any users of your code about that decision. -- -- Lou Pecora -- http://mail.python.org/mailman/listinfo/python-list
