I was assigned this problem: (which I here present verbatim)
Let $f$ be a holomorphic function of the unit disk unto itself. Prove that $|f'(0)|\le 1$.
Isn't it also necessary to assume that $f(0)=0$ for the above to be true in general?
Problem 2 of this link states it in a way that reduces to the above result when $f(0)=0$.
Thanks in advance