\begin{definition}[Definition:P-adic Unit]
Let $p$ be a prime number.
Let $\struct {\Q_p, \norm {\,\cdot\,}_p}$ be the $p$-adic numbers.
Let $\Z_p$ denote the $p$-adic integers.
The set of '''$p$-adic units''', denoted $\Z_p^\times$, is the set of invertible elements of $\Z_p$.
\end{definition}