Definition:Zero Residue Class

Definition
Let $m \in \Z$.

Let $\mathcal R_m$ be the congruence relation modulo $m$ on the set of all $a, b \in \Z$:
 * $\mathcal R_m = \left\{{\left({a, b}\right) \in \Z \times \Z: \exists k \in \Z: a = b + k m}\right\}$

Let $\left[\!\left[{0}\right]\!\right]_m$ be the residue class of $0$ (modulo $m$):
 * $\left[\!\left[{0}\right]\!\right]_m = \left\{ {x \in \Z: \exists k \in \Z: x = k m}\right\}$

Then $\left[\!\left[{0}\right]\!\right]_m$ is known as the zero residue class (modulo $m$).

Also see

 * Definition:Integers Modulo m