Equivalence relation

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Equivalence relation --- отношение эквивалентности.

A relation is an equivalence relation if it is reflexive, symmetric, and transitive. For an equivalence relation R in a set S, the equivalence class of a with respect to R is the set of all elements b in S such that aRb. When the relation R is understood, the equivalence class of a is denoted by [a]. The equivalence classes of an equivalence relation in S form a partition of S. If an equivalence relation R_{1} is contained in another equivalence relation R_{2} (i.e., if aR_{1}b implies aR_{2}b), then the partition formed by the equivalence classes with respect to R_{1} is finer than the partition formed by the classes with respect to R_{2}.