Definition:Bounded Mapping/Complex-Valued/Unbounded

Definition
Let $f: S \to \C$ be a complex-valued function.

Then $f$ is unbounded $f$ is not bounded.

That is, $f$ is unbounded if there does not exist a constant $K \ge 0$ such that $\cmod {f \paren z} \le K$ for all $z \in S$.