Partition

A partition of a set X is a set P of nonempty subsets of X such that every element x in X is in exactly one of these subsets.

Examples:

• The set {1, 2, 3} has the following partitions
  • { {1}, {2}, {3} },
  • { {1, 2}, {3} },
  • { {1, 3}, {2} },
  • { {1}, {2, 3} } and
  • { {1, 2, 3} }.

Note that { {}, {1,3}, {2} } is not a partition because it contains an empty subset and { {1,2}, {2, 3} } is also not a partition because the element 2 is contained in more than one subset.

See also:

• Equivalence relation