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# Partition

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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

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Last edited July 16, 2001 5:30 am (diff)
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