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).

Note that $1\cdot 2\cdot \ldots \cdot n\le n\cdot n\cdot \ldots \cdot n$, so we even have $n!\le n^n$.
