\begin{definition}[Definition:P-adic Integer/Definition 1]
Let $\struct {\Q_p, \norm {\,\cdot\,}_p}$ be the $p$-adic numbers for some prime $p$.
An element $x \in \Q_p$ is called a '''$p$-adic integer''' {{iff}} $\norm x_p \le 1$.
The set of all '''$p$-adic integers''' is usually denoted $\Z_p$.
Thus:
:$\Z_p = \set {x \in \Q_p: \norm x_p \le 1}$
\end{definition}