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.

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Famous quotes containing the words partitions and/or relations:

    “Walls have cracks and partitions ears.”
    —Chinese proverb.

    “What a man sows, that shall he and his relations reap.”
    —Clarissa Graves (1892–1985?)