Although slightly off-topic, it is interesting to see that some kinds of mistakes never die. As a schoolboy, I once thought that 0^0 can only take the values 0

Although slightly off-topic, it is interesting to see that some kinds of mistakes never die. As a schoolboy, I once thought that 0^0 can only take the values 0 and 1. (which is quite similar to the author's mistake to think that 0^0 is always 1) I thought so because for x → 0, 0^x → 0 x^0 → 1 x^x → 1 and I couldn't find any other expressions of the type "0^0" that have a limit different from 0 and 1. I even wrote a "proof" for it, which of course was flawed, but it took others (and me) quite some time to find the exact mistake in my "proof". 0^0 is completely indefinite in the sense that you can find "0^0" expressions for any limit a you want it to be. Here's an example for that kind of expressions: x ^ (ln a / ln x) → a Although I wasn't able to come up with those as a schoolboy, this is an easy exercise for any math student.