Definition:Canonical Epimorphism

Definition
Let $m \in \Z$.

Let $f:\Z \to \Z_m$ be a mapping such that:


 * $\forall n \in \Z: f(n) = \left[\!\left[{n}\right]\!\right]_m$

where:


 * $\Z_m$ denotes the integers modulo $m$.


 * $\left[\!\left[{n}\right]\!\right]_m$ denotes the residue class of $n$ modulo $m$.

Then $f$ is referred to as the canonical epimorphism ( from $\Z$ to $\Z_m$).

That this is an epimorphism is proved in Canonical Epimorphism is Epimorphism.