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:
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