Partition

A partition of a set \(A\) is a set \(\Pi\) consisting of subsets of \(A\) such that: - whenever \(P_1, P_2 \in \Pi\) and \(P_1 \ne P_2\) - then \(P_1 \cap P_2 = \emptyset\)

Every \(a \in A\) belongs to some \(P \in \Pi\).

Partitioning the set is the same as having an equivalence relation on the set.