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