Definition:P-adic Metric

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

Let $\left\vert{q}\right\vert_p$ 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