Definition:P-adic Metric

Definition
Let $p \in \N$ be a prime.

Let $\left\Vert{\cdot}\right\Vert_p: \Q \to \R_{\ge 0}$ be the $p$-adic norm on $\Q$.

The $p$-adic metric on $\Q$ is the metric induced by $\left\Vert{\cdot}\right\Vert_p$:


 * $\forall x, y \in \Q: d \left({x, y}\right) = \left\Vert{x - y}\right\Vert_p$

Also see

 * P-adic Metric is Metric


 * Ostrowski's Theorem