On 13/09/2013 06:41, Dan Christensen wrote: > Playing around with a calculator, I found the following:
You needed a calculator!
> If x=0 and y is a very small positive real number, then we have > x^y=0. Shifting x just slightly into the positive suddenly results in > x^y being very close to 1. > > Nothing earth-shattering here, but it seems to reinforce my > recommendation that 0^0 ought to be left undefined for any real-world > applications. f(x,y)=x^y simply behaves too strangely close to the > origin.
In other words x^y cannot be extended to a continuous function at (0,0).
So, why if your interests concern integers, does the behaviour of real a real variable function influence you so much?