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Partition of a set
Mathematical ways to group elements of a set / From Wikipedia, the free encyclopedia
This article is about grouping elements of a set. For partitioning an integer, see Integer partition. For the partition calculus of sets, see Infinitary combinatorics. For the problem of partitioning a multiset of integers so that each part has the same sum, see Partition problem.
In mathematics, a partition of a set is a grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one subset.
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Every equivalence relation on a set 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 setoid, typically in type theory and proof theory.