\begin{definition}[Definition:Bounded Metric Space/Definition 2]
Let $M = \struct {A, d}$ be a metric space.
Let $M' = \struct {B, d_B}$ be a subspace of $M$.
$M'$ is '''bounded''' {{iff}}:
:$\exists K \in \R: \forall x, y \in M': \map {d_B} {x, y} \le K$
That is, there exists a finite distance such that all pairs of elements of $B$ are within that distance.
\end{definition}