partitionPartition2001-10-19 01:04:092007-03-07 17:13:15Definition\usepackage{amssymb}
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A \emph{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 $S$.