Definition:P-adic Norm

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

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

Also see

 * Rational Numbers are Dense Subfield of P-adic Numbers for a proof that the $p$-adic norm on $p$-adic numbers may be considered an extension of the $p$-adic norm on the rational numbers