Definition:Set of Integer Multiples

Definition
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:
 * $n \Z = \set {\ldots, -3 n, -2 n, -n, 0, n, 2 n, 3 n, \ldots}$

Also see

 * Definition:Principal Ideal of Ring