Solution
= Solution
This is an equivalence relation: $x-x=0\in\mathbb Z$; if $x-y\in\mathbb Z$, then $y-x\in\mathbb Z$; and integer differences add. Its classes are
$$
\boxed{[x]=x+\mathbb Z},
$$
the cosets of $\mathbb Z$ in $\mathbb R$.
= Solution
This is an equivalence relation: $x-x=0\in\mathbb Z$; if $x-y\in\mathbb Z$, then $y-x\in\mathbb Z$; and integer differences add. Its classes are
$$
\boxed{[x]=x+\mathbb Z},
$$
the cosets of $\mathbb Z$ in $\mathbb R$.