Changes

3. Transitive: if a~b and b~c, then a~c.

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.

[[Equality]] and set [[member]]ship 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]]s.  

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'''.

An equivalence relation on a set S [[partition]]s 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]].

Equivalence relations are the mathematical foundation for forming [[quotient]]s.

[[Category:Mathematics]]

[[Category:Mathematics]]