Show that $n! = O(n^{n})$ As the title says, how would you show that $n! = O(n^{n})$? I'm not really understanding how one "shows" the Big O notation of a function mathematically (at least when you're dealing with things that aren't polynomials).

If $k \le n$, then $k \le n$ :-). That is $\prod_{k=1}^n k \le \prod_{k=1}^n n = n^n$.
