Definition:Set of Integer Multiples

Definition

The set $n \Z$ is defined as:

$\left\{{x \in \Z: n \backslash x}\right\}$

for some $n \in \N$.

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:

$n \Z = \left\{{\ldots, -3n, -2n, -n, 0, n, 2n, 3n, \ldots}\right\}$

Sources

• J.A. Green: Sets and Groups (1965)... (previous)... (next): $\S 5.2$: Example $92$