# Definition:Bounded Mapping/Complex-Valued/Unbounded

Let $f: S \to \C$ be a complex-valued function.
Then $f$ is unbounded if and only if $f$ 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 $z \in S$.