# Definition:Zero Residue Class

## Definition

Let $m \in \Z$.

Let $\mathcal R_m$ be the congruence relation modulo $m$ on the set of all $a, b \in \Z$:

$\mathcal R_m = \set {\tuple {a, b} \in \Z \times \Z: \exists k \in \Z: a = b + k m}$

Let $\eqclass 0 m$ be the residue class of $0$ (modulo $m$):

$\eqclass 0 m = \set {x \in \Z: \exists k \in \Z: x = k m}$

Then $\eqclass 0 m$ is known as the zero residue class (modulo $m$).