\begin{definition}[Definition:Bounded Normed Vector Space/Definition 1]
Let $M = \struct {X, \norm {\, \cdot \,}}$ be a normed vector space.
Let $M' = \struct {Y, \norm {\, \cdot \,}_Y}$ be a subspace of $M$.
'''$M'$ is bounded (in $M$)''' {{iff}}:
:$\exists x \in X, C \in \R_{> 0}: \forall y \in Y: \norm {x - y} \le C$
\end{definition}