Prove log(n!) is O(nlogn)

In this video, I will show you how to prove or disprove Big O. For example, you are asked to prove that a function log(n!) is O(nlogn). By the definition of big O, f(n) is O(g(n)) if you can find a positive constant c and a positive integer nₒ such that f(n) is less than or equal to c times g(n), for all n is greater than nₒ.

Knowing how to prove that something is Big O or not Big O is an important skill that Computer Science CS and Math students need to know about time complexity and growth of functions. It is likely that you will encounter this topic in your typical Data Structures, Discrete Mathematics, or Analysis of Algorithm courses at University.

I will also how you how to prove Big Omega Ω or Big Theta θ. If you enjoyed this video, please don't forget to comment down below and also subscribe if you haven't already!