Definition:P-adic Norm

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

Also see

 * $p$-adic Norm is Norm where it is shown that the $p$-adic norm is a norm on a division ring.


 * $p$-adic Norm is non-Archimedean Norm where it is shown that the $p$-adic norm is a non-Archimedean norm on a division ring.


 * $p$-adic Norm and Absolute Value are Not Equivalent where it is shown that the $p$-adic norm yields a different topology on the rationals from the usual Euclidean Metric.


 * $p$-adic Norms are Not Equivalent where it is shown that the $p$-adic norms for two distinct prime numbers are not equivalent norms.


 * Equivalence of Definitions of P-adic Norms