Definition:P-adic Valuation/P-adic Numbers

Definition
Let $p$ be a prime number. Let $\struct {\Q_p, \norm {\,\cdot\,}_p}$ be the $p$-adic numbers.

Also see

 * Equivalence of Definitions of P-adic Valuation on P-adic Numbers


 * P-adic Valuation Extends to P-adic Numbers where it is shown that $\nu_p$ is a valuation that extends the $p$-adic valuation on the rational numbers $\Q$ to $\Q_p$.