Definition:P-adic Metric

Definition
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 $\norm{\cdot}_p$:


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

$p$-adic Numbers
Let $\struct{\Q_p,\norm{\,\cdot\,}_p}$ be the $p$-adic numbers.

Also see

 * P-adic Metric is Metric


 * Ostrowski's Theorem