Partition of a set

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.

This article is about grouping elements of a set. For partitioning an integer, see Partition (number theory). For the partition calculus of sets, see Infinitary combinatorics.

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.

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