Partitions#

Definition: Partition

A partition of a set \(S\) is a collection \(\mathcal{P}\) of subsets of \(S\) with the following properties:

• non-emptiness: \(\mathcal{P} \ne \varnothing\);
• pairwise disjointness: \(A \cap B = \varnothing\) for all \(A, B \in \mathcal{P}\);
• covering: \(S = \bigcup \mathcal{P}\).