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Equivalence relation
Mathematical concept for comparing objects / From Wikipedia, the free encyclopedia
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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. A simpler example is equality. Any number is equal to itself (reflexive). If
, then
(symmetric). If
and
, then
(transitive).
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![]() ![]() All definitions tacitly require the homogeneous relation |
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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.