# Equivalence Class Set

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An Equivalence Class Set is a two-or-more member set whose members are in an equivalence relation.

**See:**Quotient Category, Subset, Partition of a Set, Quotient Space, Quotient Group, Homogeneous Space, Quotient Ring, Quotient Monoid.

## References

### 2015

- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/equivalence_class Retrieved:2015-6-2.
- In mathematics, when a set has an equivalence relation defined on its elements, there is a natural grouping of elements that are related to one another, forming what are called '
*equivalence classes. Notationally, given a set and an equivalence relation ~ on, the*equivalence class*of an element in is the subset of all elements in which are equivalent to . It follows from the definition of the equivalence relations that the equivalence classes form a partition of. The set of equivalence classes is sometimes called the*X / ~.**quotient set**or the quotient space of by ~ and is denoted byWhen has some structure, and the equivalence relation is defined with some connection to this structure, the quotient set often inherits some related structure. Examples include quotient spaces in linear algebra, quotient spaces in topology, quotient groups, homogeneous spaces, quotient rings, quotient monoids, and quotient categories.

- In mathematics, when a set has an equivalence relation defined on its elements, there is a natural grouping of elements that are related to one another, forming what are called '