Definition:Restricted Dipper Relation

Definition
Let $m, n \in \N_{>0}$ be non-zero natural numbers.

The restricted dipper relation $\RR^*_{m, n}$ is the restriction of the dipper relation $\RR_{m, n}$ on $\N$:


 * $\forall x, y \in \N_{>0}: x \mathrel {\RR^*_{m, n} } y \iff \begin {cases} x = y \\ m \le x < y \text { and } n \divides \paren {y - x} \\ m \le y < x \text { and } n \divides \paren {x - y} \end {cases}$

Also see

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


 * Definition:Dipper Relation