\begin{definition}[Definition:P-adic Metric/P-adic Numbers]
Let $p \in \N$ be a prime.
Let $\struct{\Q_p,\norm{\,\cdot\,}_p}$ be the $p$-adic numbers.
The '''$p$-adic metric''' on $\Q_p$ is the metric induced by $\norm{\cdot}_p$:
:$\forall x, y \in \Q_p: \map d {x, y} = \norm{x - y}_p$
\end{definition}