Equivalence classes of equivalence relation

Reference no: EM13132405

Modern Algebra

Set Theory (II)

Equivalence Classes of an Equivalence Relation

The distinct equivalence classes of an equivalence relation on a set A provide us with a decomposition of A as a union of mutually disjoint subsets.

Conversely, given a decomposition of A as a union of mutually disjoint, nonempty subsets, we can define an equivalence relation on A for which these subsets are the distinct equivalence classes.

Or, An equivalence relation over a set induces a partition of the set. Conversely, a partition of a set defines an equivalence relation.

Reference no: EM13132405

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