Could someone please help me prove the following and tell me their thought process as well if possible?
Let $f$ be a continuous real-valued function on the closed, bounded subset $S$ of the complex plane. Use the Bolzano-Weierstrass Theorem to show that $f$ is bounded.
The hint given was: "If this is not the case then there exists a sequence of points $z_n \in S$ such that $f(z_n)>n$.
Any kind of help will be much appreciated!