\begin{definition}[Definition:Set of Residue Classes]
Let $m \in \Z$.
Let $\RR_m$ be the congruence relation modulo $m$ on the set of all $a, b \in \Z$:
:$\RR_m = \set {\tuple {a, b} \in \Z \times \Z: \exists k \in \Z: a = b + k m}$
Let $\eqclass a m$ be the residue class of $a$ (modulo $m$).
The quotient set of congruence modulo $m$ denoted $\Z_m$ is:
:$\Z_m = \dfrac \Z {\RR_m}$
\end{definition}