\begin{definition}[Definition:Convergent Sequence/Normed Division Ring/Definition 4]
Let $\struct {R, \norm {\, \cdot \,} }$ be a normed division ring.
Let $\sequence {x_n} $ be a sequence in $R$.
The sequence $\sequence {x_n}$ '''converges to the limit $x \in R$ in the norm $\norm {\, \cdot \,}$''' {{iff}}:
:$\sequence {x_n}$ converges to $x$ in the topology induced by the norm $\norm {\, \cdot \,}$
\end{definition}