Equivalence relations - definition. What is Equivalence relations
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%ما هو (من)٪ 1 - تعريف

REFLEXIVE, SYMMETRIC AND TRANSITIVE RELATION
EquivalenceRelation; Graphing equivalence; Equivalency; Identification (mathematics); Equivalence relations; ≍; Geometric equivalence; ≎; ≭; ≑; Fine (mathematics); Fundamental theorem of equivalence relations
  • logical matrices]] (colored fields, including those in light gray, stand for ones; white fields for zeros). The row and column indices of nonwhite cells are the related elements, while the different colors, other than light gray, indicate the equivalence classes (each light gray cell is its own equivalence class).

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.

ويكيبيديا

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.