\begin{definition}[Definition:Modulo Addition/Definition 1]
Let $m \in \Z$ be an integer.
Let $\Z_m$ be the set of integers modulo $m$:
:$\Z_m = \set {\eqclass 0 m, \eqclass 1 m, \ldots, \eqclass {m - 1} m}$
where $\eqclass x m$ is the residue class of $x$ modulo $m$.
The operation of '''addition modulo $m$''' is defined on $\Z_m$ as:
:$\eqclass a m +_m \eqclass b m = \eqclass {a + b} m$
\end{definition}