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-emptysubsets, in such a way that every element is included in exactly one subset.
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.
^Knuth, Donald E. (2013), "Two thousand years of combinatorics", in Wilson, Robin; Watkins, John J. (eds.), Combinatorics: Ancient and Modern, Oxford University Press, pp. 7–37