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partition (Definition)

A partition $ P$ of a set $ S$ is a collection of pairwise disjoint nonempty sets such that $ \cup P = S$.

Any partition $ P$ of a set $ S$ introduces an equivalence relation on $ S$, where each $ A \in P$ is an equivalence class. Similarly, given an equivalence relation on $ S$, the collection of distinct equivalence classes is a partition of $ S$.



"partition" is owned by Wkbj79. [ full author list (2) | owner history (1) ]
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See Also: equivalence relation, equivalence class, Beatty's theorem, coloring

Other names:  set partition

Attachments:
partition is equivalent to an equivalence relation (Derivation) by CWoo
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Cross-references: equivalence class, equivalence relation, pairwise disjoint, collection
There are 39 references to this entry.

This is version 6 of partition, born on 2001-10-19, modified 2007-03-07.
Object id is 362, canonical name is Partition.
Accessed 10335 times total.

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AMS MSC: 03-00 (Mathematical logic and foundations :: General reference works )
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