On Friday, September 13, 2013 4:56:07 AM UTC-4, Peter Percival wrote: > Dan Christensen wrote: > > > > > Playing around with a calculator, I found the following: > > > > > > 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. > > >
Put another way: For very small positive values of x and y, x^y can be very close to 1. If x actually becomes 0, then x^y drops to 0. If both become zero, the result is ambiguous (see above).
> > > 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. > > > > > > Comments? > > > > You've changed the question, haven't you? Didn't it start out as what > > is 0^0 in the natural numbers? > > Now it seems you're talking about reals >