\begin{definition}[Definition:Complete Residue System]
Let $m \in \Z_{\ne 0}$ be a non-zero integer.
Let $S := \set {r_1, r_2, \dotsb, r_s}$ be a set of integers with the properties that:
:$(1): \quad i \ne j \implies r_i \not \equiv r_j \pmod m$
:$(2): \quad \forall n \in \Z: \exists r_i \in S: n \equiv r_i \pmod m$
Then $S$ is a '''complete residue system modulo $m$'''.
\end{definition}