Partition of A Set - Partitions and Equivalence Relations

Partitions and Equivalence Relations

For any equivalence relation on a set X, the set of its equivalence classes is a partition of X. Conversely, from any partition P of X, we can define an equivalence relation on X by setting x ~ y precisely when x and y are in the same part in P. Thus the notions of equivalence relation and partition are essentially equivalent.

Read more about this topic:  Partition Of A Set

Famous quotes containing the words partitions and/or relations:

    “Great wits are sure to madness near allied,
    And thin partitions do their bounds divide.”
    —John Dryden (1631–1700)

    “In the relations of a weak Government and a rebellious people there comes a time when every act of the authorities exasperates the masses, and every refusal to act excites their contempt.”
    —John Reed (1887–1920)