partition

A partition $P$ of a set $S$ is a collection of pairwise disjoint nonempty sets such that $\cup P=S$.

Any partition $P$ of a set $S$ introduces an equivalence relation on $S$, where each $A\in P$ is an equivalence class. 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	Coloring