Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 4 / 2E / iii

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 arethe cosets of $\mathbb{Z}$ in $\mathbb{R}$.