A partitionMathworldPlanetmathPlanetmath P of a set S is a collectionMathworldPlanetmath of pairwise disjoint nonempty sets such that P=S.

Any partition P of a set S introduces an equivalence relationMathworldPlanetmath on S, where each AP is an equivalence classMathworldPlanetmath. Similarly, given an equivalence relation on S, the collection of distinct equivalence classes is a partition of S.

Title partition
Canonical name Partition
Date of creation 2013-03-22 11:49:05
Last modified on 2013-03-22 11:49:05
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 11
Author Wkbj79 (1863)
Entry type Definition
Classification msc 03-00
Classification msc 45D05
Synonym set partition
Related topic EquivalenceRelation
Related topic EquivalenceClass
Related topic BeattysTheorem
Related topic ColoringMathworldPlanetmath