The question is:
Show that $$\log_2(n!)\in O(n \log_2(n)).$$
I'm guessing I'll have to use principle of simple induction for this one. But how would I go about writing the proof for this? Should I use proof by cases?
What will be my first assumption? Usually the other proofs I wrote, there was a domain assumption and I assume x in set of integers, etc. Not sure what to write for this one.
Thanks for your help!