Are there any contexts where it's more useful to define 0^0 as something other than 1?

Question

0^0 is usually defined to be 1, especially in contexts like combinatorics, but it's usually left undefined in cases like analysis. So are there any situations where it's more useful to say 0^0 = 0 or 2 or anything other than 1?

Answer 1

Not that I'm aware of. I've only ever seen it as either left "undefined" or defined to be 1. Defining 0^0 = 0 wouldn't be terribly useful, since it allows a couple of limits and properties to hold, but violates many more. Anything else would have to be a pretty darn weird field of mathematics to arrive at any defined conclusion other than 1.

Answer 2

no, probably not.