section_path: Partitions
section_name: Partitions
paragraph_text: Partitions
  
  A partition of a set S is a set of nonempty subsets of S, such that every element x in S is in exactly one of these subsets. That is, the subsets are pairwise disjoint (meaning any two sets of the partition contain no element in common), and the union of all the subsets of the partition is S.