Definition:P-adic Metric/Rational Numbers
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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 $\norm{\cdot}_p$:
- $\forall x, y \in \Q: \map d {x, y} = \norm {x - y}_p$