Complete residue system ($\{a_1,\dots ,a_m\}⟶\mathbb{Z}/m\mathbb{Z}\text{ bijectively}$)

A complete residue system modulo a positive integer $m$ contains exactly one representative of every congruence class modulo $m$. Both $\{0,\dots ,m-1\}$ and $\{1,\dots ,m\}$ are examples. Counting the representatives that are coprime to $m$ gives Euler's totient function; those representatives form a reduced residue system.