In any case, I agree with Yee in that it’s a matter of definition. The most common scenario, in my experience, is that 0^0 is defined and equal to 1. That’s not to say that some don’t choose to define 0^0 as 0 (or something else, or even leave it undefined). In fact, there are probably authors who will handle it differently depending on what they are working on.

As to your point about no proof existing that shows 0^0 = 1, why do you require one? I’m assuming you agree that 1+1 = 2, but have you ever asked for a proof of that? What if I’m a computer scientist so I define things such that 1+1 = 10 (and the symbol “2″ has no meaning in my world)?

Math is, very broadly, about defining constructs on top of a set of axioms and applying logic to them to get useful results. As the original post points out, depending on your choice of definition of x^y for x,y > 0, the value of 0^0 may be a natural extension. Or you might just arbitrarily choose o^o = 1 to make things “nicer.”

It’s like someone ran an astronomy text through google translate.