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What (who) is Equivalence relations - definition
REFLEXIVE, SYMMETRIC AND TRANSITIVE RELATION
EquivalenceRelation; Graphing equivalence; Equivalency; Identification (mathematics); Equivalence relations; ≍; Geometric equivalence; ≎; ≭; ≑; Fine (mathematics); Fundamental theorem of equivalence relations
equivalence relation
<mathematics> A relation R on a set including elements a, b,
c, which is reflexive (a R a), symmetric (a R b => b R a) and
transitive (a R b R c => a R c). An equivalence relation
defines an equivalence class.
See also partial equivalence relation.
(1996-05-13)
equivalence relation
¦ noun Mathematics & Logic a relation between elements of a set which is reflexive, symmetric, and transitive and which defines exclusive classes whose members bear the relation to each other and not to those in other classes.
Equivalency
·noun ·same·as Equivalence.
Wikipedia
Equivalence relation
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in geometry is a common example of an equivalence relation.
Each equivalence relation provides a partition of the underlying set into disjoint equivalence classes. Two elements of the given set are equivalent to each other if and only if they belong to the same equivalence class.
