Equivalence relation

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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 numerical equality. Any number a {\displaystyle a} is equal to itself (reflexive). If a = b {\displaystyle a=b} , then b = a {\displaystyle b=a} (symmetric). If a = b {\displaystyle a=b} and b = c {\displaystyle b=c} , then a = c {\displaystyle a=c} (transitive). 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...

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