## Definition

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 $z$.

## Also denoted as

Although the operation of addition modulo $z$ is denoted by the symbol $+_z$, if there is no danger of confusion, the symbol $+$ is often used instead.

The notation for addition of two residue classes modulo $z$ is not usually $\eqclass a z +_z \eqclass b z$.

The usual notation is $a + b \pmod z$.