\begin{definition}[Definition:Complete Normed Division Ring]
A normed division ring $\struct {R, \norm {\, \cdot \,} }$ is '''complete''' {{iff}} the metric space $\struct {R, d}$ is a complete metric space where $d$ is the metric induced by the norm $\norm {\, \cdot \,}$.
That is, a normed division ring $\struct {R, \norm {\, \cdot \,} }$ is '''complete''' {{iff}} every Cauchy sequence is convergent.
\end{definition}