Idempotent relation
In mathematics, an idempotent binary relation is a binary relation R on a set X (a subset of Cartesian product X × X) for which the composition of relations R ∘ R is the same as R. This notion generalizes that of an idempotent function to relations. == Definition == As a shorthand, the notation xRy indicates that a pair (x,y) belongs to a relation R. The composition of relations R ∘ R is the relation S defined by setting xSz to be true for a pair of elements x and z in X whenever there exists y in X with xRy and yRz both true.