\begin{definition}[Definition:Metric Induced by Norm on Division Ring]
Let $\struct {R, \norm {\,\cdot\,} }$ be a normed division ring.
Then the '''induced metric''' or the '''metric induced by $\norm {\,\cdot\,}$''' is the map $d: R \times R \to \R_{\ge 0}$ defined as:
:$d \paren {x, y} = \norm {x - y}$
\end{definition}