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Reference.org
Partition of a set
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a partition of a set is a grouping of its elements into <a href="/facts/Empty_set/ffEk3eA6">non-empty</a> <a href="/facts/Subset/SJGERmbA">subsets</a>, in such a way that every element is included in exactly one subset. </p><p>Every <a href="/facts/Equivalence_relation/1MQ5rtkW">equivalence relation</a> on a <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> defines a partition of this set, and every partition defines an equivalence relation. A set equipped with an equivalence relation or a partition is sometimes called a <a href="/facts/Setoid/oJUssDY7">setoid</a>, typically in <a href="/facts/Type_theory/xj0xzVqI">type theory</a> and <a href="/facts/Proof_theory/kopBdQn9">proof theory</a>. </p>