In the course of the craziness about the whole you know what (see the links in the sidebar), it somehow came up that 0^0 (which is to say, 0 to the 0-eth power) is a tricky calculation. Several commenters gave their opinions, and so, for fun, here's mine. Consider the following chart:
Note that negative and zero exponents are pretty much defined to make each column's pattern (successive division by the base for that column) continue. And when you do define it that way, lo and behold, the standard laws of exponents hold, and we're therefore happy with that definition. That's how math works, right? We find patterns and see if our codifications of them continue to make sense after they get more and more abstract.
The problem with 0^0 is that it seems to have to satisfy two patterns at once. The column pattern is that the right hand side is always 0. The row pattern is that the right hand side is always 1. So what goes in the green box? 1 or 0? Both continue a pattern.
Take a look, though, at the entries in the blue column below the green box. Since 0 can't appear in a denominator, those entries are missing. Thus, crucially, the pattern in the blue column will have to end anyway. So if our goal for this definition is to preserve as many patterns as possible, we don't lose much pattern by saying that 0^0 is 1. That preserves the horizontal yellow pattern, and breaks the vertical blue pattern, but...hey, it was broken soon anyway.
So that's my vote and my reason. 0^0 should be defined as 1.
You might be a geek if....you devote a whole blog post to this.