\begin{definition}[Definition:Set of Integer Multiples]
The set $n \Z$ is defined as:
:$\set {x \in \Z: n \divides x}$
for some $n \in \Z_{>0}$.
That is, it is the set of all integers which are divisible by $n$, that is, the '''set of integer multiples of $n$'''.
Thus we have:
:$n \Z = \set {\ldots, -3 n, -2 n, -n, 0, n, 2 n, 3 n, \ldots}$
\end{definition}