# 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