Definition
A partition of a set X is a set of nonempty subsets of X such that every element x in X is in exactly one of these subsets.
Equivalently, a set P is a partition of X if, and only if, it does not contain the empty set and:
- The union of the elements of P is equal to X. (The elements of P are said to cover X.)
- The intersection of any two distinct elements of P is empty. (We say the elements of P are pairwise disjoint.)
In mathematical notation, these two conditions can be represented as
- 1.
- 2.
where is the empty set.
The elements of P are called the blocks, parts or cells of the partition.
The rank of P is |X| − |P|, if X is finite.
Read more about this topic: Partition Of A Set
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