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# 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 $S$.

Related:

EquivalenceRelation, EquivalenceClass, BeattysTheorem, Coloring

Synonym:

set partition

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

03-00*no label found*45D05

*no label found*

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