\begin{definition}[Definition:Bounded Sequence/Normed Vector Space]
Let $\struct {X, \norm {\, \cdot \,} }$ be a normed vector space.
Let $\sequence {x_n}$ be a sequence in $X$.
Then $\sequence {x_n}$ is '''bounded''' {{iff}}:
:$\exists K \in \R$ such that $\forall n \in \N: \norm {x_n} \le K$
\end{definition}