Definition:Dipper Relation

Definition
Let $m \in \N$ be a natural number.

Let $n \in \N_{>0}$ be a non-zero natural number.

The dipper relation $\RR_{m, n}$ is the be the relation on $\N$ defined as:


 * $\forall x, y \in \N: x \mathrel {\RR_{m, n} } y \iff \begin {cases} x = y \\ m \le x < y \text { and } n \divides \paren {y - x} \\ m \le y < x \text { and } n \divides \paren {x - y} \end {cases}$

Also see

 * Dipper Relation is Equivalence Relation
 * Dipper Relation is Congruence for Addition
 * Dipper Relation is Congruence for Multiplication