In mathematics, there are two different notions of a ring of sets, both referring to certain families of sets. In order theory, a nonempty family of sets is called a ring (of sets) if it is closed under intersection and union. That is, for any ,
- and
In measure theory, a ring of sets is instead a family closed under unions and set-theoretic differences. That is, it obeys the two properties
- and
This implies that it is also closed under intersections, because of the identity
however, a family of sets that is closed under unions and intersections might not be closed under differences.
Read more about Ring Of Sets: Examples, Related Structures
Famous quotes containing the words ring and/or sets:
“The life of man is a self-evolving circle, which, from a ring imperceptibly small, rushes on all sides outwards to new and larger circles, and that without end.”
—Ralph Waldo Emerson (1803–1882)
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—William Bolitho (1890–1930)