Definition:Addition/Real Modulo Addition

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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 $a + b \pmod z$.

Also see