Definition:P-adic Metric/P-adic Numbers

Definition
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 $\norm{\cdot}_p$:


 * $\forall x, y \in \Q: \map d {x, y} = \norm{x - y}_p$

The $p$-adic numbers $\Q_p$ contains the rationals numbers $\Q$ (disregarding isomorphisms), and the $p$-adic metric on $\Q_p$ is an extension of the $p$-adic metric on $\Q$.

Also See

 * P-adic Metric on P-adic Numbers is Metric