equivalence relation

In mathematics, an equivalence relation is a binary relation between two elements of a set which groups them together as being "equivalent" in some way. That a is equivalent to b is denoted as "a ~ b" or "a ≡ b". An equivalence relation is reflexive, symmetric, and transitive. In other words, for all elements a, b, and c of the set X, the following must hold for "~" to be an equivalence relation on X: Reflexivity: a ~ aSymmetry: if a ~ b then b ~ aTransitivity: if a ~ b and b ~ c then a ~ c.
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<mathematics a R c). An equivalence relation defines an equivalence class.
See also partial equivalence relation.
(1996-05-13)

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