P-adic Unit has Norm Equal to One

Definition
Let $\norm {\,\cdot\,}_p$ be the $p$-adic norm on the $p$-adic numbers $\Q_p$ for some prime $p$.

The set of $p$-adic units, denoted $\Z_p^\times$, is the set:
 * $\Z_p^\times = \set {x \in \Q_p: \norm x_p = 1}$