I know this is a stupid question but I will ask it anyway. I need to do complexity analysis for n! to prove that it is not a certain complexity order. How can I go about doing that?
Problem: Prove that $n!$ is not O($2^n$).
I'm not sure how I can start this problem. I want to say that I could compare the factorial to the complexity order in an inequality. This confuses me because they are basically two different values.