\begin{definition}[Definition:P-adic Integer/Definition 2]
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}} the canonical expansion of $x$ contains only positive powers of $p$.
The set of all '''$p$-adic integers''' is usually denoted $\Z_p$.
Thus:
:$\ds \Z_p = \set {\sum_{n \mathop = 0}^\infty d_n p^n : \forall n \in \N: 0 \le d_n < p} = \set{\ldots d_n \ldots d_3 d_2 d_1 d_0 : \forall n \in \N: 0 \le d_n < p}$
\end{definition}