= Additive group of integers
{title2=$(\mathbb Z,+)$}
= Group of integers
{synonym}
The <integers> form an <infinite cyclic group> under addition, with <identity element> zero and <inverse element> $-n$ for $n$. Its two generators are $1$ and $-1$. Every <subgroup> is $m\mathbb Z$ for a unique nonnegative integer $m$: if it is nonzero, take its least positive element and use division with remainder to show that every element is a multiple of it. The zero subgroup corresponds to $m=0$.
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