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:
“He will not idly dance at his work who has wood to cut and cord before nightfall in the short days of winter; but every stroke will be husbanded, and ring soberly through the wood; and so will the strokes of that scholar’s pen, which at evening record the story of the day, ring soberly, yet cheerily, on the ear of the reader, long after the echoes of his axe have died away.”
—Henry David Thoreau (1817–1862)
“The poem has a social effect of some kind whether or not the poet wills it to have. It has kinetic force, it sets in motion ... [ellipsis in source] elements in the reader that would otherwise be stagnant.”
—Denise Levertov (b. 1923)