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)
“The interest in life does not lie in what people do, nor even in their relations to each other, but largely in the power to communicate with a third party, antagonistic, enigmatic, yet perhaps persuadable, which one may call life in general.”
—Virginia Woolf (1882–1941)