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Equivalence relation (view source)
Revision as of 19:35, February 17, 2008
, 19:35, February 17, 2008basic concept of mathematics
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.
[[Congruence|Congruence relations]] are examples of equivalence relations, as is the j-invariant of [[Elliptic_curve|elliptic curves]].
An equivalence relation on a set S [[Partition|partitions]] S into [[disjoint]] subsets, known as ''equivalence classes''. Two objects in the same equivalence class are said to be ''equivalent''.
Equivalence relations are the mathematical foundation for forming [[Quotient|quotients]].
[[Congruence|Congruence relations]] are examples of equivalence relations, as is the j-invariant of [[Elliptic_curve|elliptic curves]].
An equivalence relation on a set S [[Partition|partitions]] S into [[disjoint]] subsets, known as ''equivalence classes''. Two objects in the same equivalence class are said to be ''equivalent''.
Equivalence relations are the mathematical foundation for forming [[Quotient|quotients]].