Modulo Addition has Identity

Theorem
Let $m \in \Z$ be an integer.

Then addition modulo $m$ has an identity:


 * $\forall \eqclass x m \in \Z_m: \eqclass x m +_m \eqclass 0 m = \eqclass x m = \eqclass 0 m +_m \eqclass x m$

That is:
 * $\forall a \in \Z: a + 0 \equiv a \equiv 0 + a \pmod m$

Proof
Thus $\eqclass 0 m$ is the identity for addition modulo $m$.