Equivalence relation

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 if and only if they belong to the same equivalence class.