\begin{definition}[Definition:Addition/Real Modulo Addition]
Let $z \in \R$.
Let $\R_z$ be the set of residue classes modulo $z$ of $\R$.
The addition operation is defined on $\R_z$ as follows:
:$\eqclass a z +_z \eqclass b z = \eqclass {a + b} z$
This operation is called '''addition modulo $z$'''.
\end{definition}