\begin{definition}[Definition:Bounded Metric Space/Complex/Unbounded]
Let $D$ be a subset of the complex plane $\C$.
Then '''$D$ is unbounded (in $\C$)''' {{iff}}:
: $\nexists M \in \R: \forall z \in D: \cmod z \le M$
That is, if $D$ is not bounded in $\C$.
\end{definition}