Concept

Equivalence relation

Summary
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. Notation Various notations are used in the literature to denote that two elements a and b of a set are equivalent with respect to an equivalence relation R; the most common are "a \sim b" and "a ≡ b", which are used when R is implicit, and variations of "a \sim_R b", "a ≡R b", or "{a\mathop{R}b}" to specify R explicitly. Non-equivalence may be written "a ≁ b" or "a \not\equiv b". Definition A binary relation ,\si
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