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.