# Definition:Bounded Metric Space/Complex

## Definition

Let $D$ be a subset of the complex plane $\C$.

Then $D$ is bounded (in $\C$) if and only if there exists $M \in \R$ such that:

$\forall z \in D: \cmod z \le M$

## Unbounded

Let $D$ be a subset of the complex plane $\C$.

Then $D$ is unbounded (in $\C$) if and only if:

$\nexists M \in \R: \forall z \in D: \cmod z \le M$

That is, if $D$ is not bounded in $\C$.