\begin{definition}[Definition:P-adic Metric/Rational Numbers]
Let $p \in \N$ be a prime.
Let $\norm {\cdot}_p: \Q \to \R_{\ge 0}$ be the $p$-adic norm on $\Q$.
The '''$p$-adic metric''' on $\Q$ is the metric induced by $\norm{\cdot}_p$:
:$\forall x, y \in \Q: \map d {x, y} = \norm {x - y}_p$
\end{definition}