This question doesn't have an answer because, as this post suggests, the meanings of the first 0, the second 0, and the (^) are overloaded. The reason mathemati

This question doesn't have an answer because, as this post suggests, the meanings of the first 0, the second 0, and the (^) are overloaded. The reason mathematicians don't mind the overloading is that they all have "kind of" similar meanings. So we can talk about a recursively defined function on naturals where it's convenient to "define" 0^0 = 1. We can talk about various kinds of limit techniques in the reals where 0^0 is not actually a value but instead a shorthand for a particular kind of limit. This probably forms the most interesting notion of what 0^0 means where we define it as the limit of a particular kind of path in the complex plane and then notice that 0^0 can take any value we choose---depending on exactly what path was taken to get there. [0] [0] http://en.wikipedia.org/wiki/Complex_logarithm http://en.wikipedia.org/wiki/Complex_logarithm