A division of a set into nonempty disjoint sets that completely cover the set. In other words, a partition P of a set S is a set of subsets with the following properties:

• ∀ s_i ∈ P, s_i ≠ ø
  (no subset is empty),
• ∀ s_i, s_j ∈ P, i ≠ j → s_i ∩ s_j = ø
  (subsets are disjoint), and
• U_i=1 s_i = S
  (subsets exactly cover the original).