Definition:Complete Normed Division Ring

Definition
A normed division ring $\struct {R, \norm {\, \cdot \,} }$ is complete 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 every Cauchy sequence is convergent.