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An '''equivalence relation''' is a mathematical [[relation]] which is [[Reflexivity|reflexive]], [[Symmetry|symmetric]], and [[Transitivity|transitive]]. [[Equality]] and set [[Member|membership]] are the most basic equivalence relations, which is why they are often called trivial equivalence relations. Every equivalence relation is constructed from [[Irreducibility|irreducible]] equivalences.
An '''equivalence relation''' is a mathematical [[relation]] (denoted by ~) which is [[Reflexivity|reflexive]], [[Symmetry|symmetric]], and [[Transitivity|transitive]].
1. Reflexive: a~a.
2. Symmetric: if a~b then b~a.
3. Transitive: if a~b and b~c, then a~c.
[[Equality]] and set [[Member|membership]] are the most basic equivalence relations, which is why they are often called trivial equivalence relations. Every equivalence relation is constructed from [[Irreducibility|irreducible]] equivalences.
[[Congruence|Congruence relations]] are examples of equivalence relations, as is the j-invariant of [[Elliptic_curve|elliptic curves]].
[[Congruence|Congruence relations]] are examples of equivalence relations, as is the j-invariant of [[Elliptic_curve|elliptic curves]].