I have done a lot of math so far, but I never stumbled on something this simple and yet mind boggling. Can someone tell me why $0^0$ equals $1$? I always knew that everything raised to a power of $0$ is $1$, but I never thought of the zero case itself.
I guess it's not the biggest problem in math, but I would like to have a good argument about why a $0$ can be turned into a $1$?
This depends on the situation. $0^0$ is often considered an indeterminate form. I believe a combinatorial interpretation leads to $0^0=1$. Namely that the number of total outcomes from $m$ events with $k$ outcomes each is $k^m$. Thus zero events having zero outcomes each still produce $1$ total outcome and so $0^0=1$.