Category:Examples of Set Partitions
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This category contains examples of Set Partition.
Let $S$ be a set.
Definition 1
A partition of $S$ is a set of subsets $\Bbb S$ of $S$ such that:
- $(1): \quad$ $\Bbb S$ is pairwise disjoint: $\forall S_1, S_2 \in \Bbb S: S_1 \cap S_2 = \O$ when $S_1 \ne S_2$
- $(2): \quad$ The union of $\Bbb S$ forms the whole set $S$: $\ds \bigcup \Bbb S = S$
- $(3): \quad$ None of the elements of $\Bbb S$ is empty: $\forall T \in \Bbb S: T \ne \O$.
Definition 2
A partition of $S$ is a set of non-empty subsets $\Bbb S$ of $S$ such that each element of $S$ lies in exactly one element of $\Bbb S$.
Pages in category "Examples of Set Partitions"
The following 12 pages are in this category, out of 12 total.
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- Total Number of Set Partitions/Examples
- Total Number of Set Partitions/Examples/2
- Total Number of Set Partitions/Examples/2/Illustration
- Total Number of Set Partitions/Examples/3
- Total Number of Set Partitions/Examples/3/Illustration
- Total Number of Set Partitions/Examples/4
- Total Number of Set Partitions/Examples/4/Illustration