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In set theory, the intersection of two sets and , denoted by , [1] is the set containing all elements of that also belong to or equivalently, all elements of that also belong to . [2] Notation and terminology
It is the algebra of the set-theoretic operations of union, intersection and complementation, and the relations of equality and inclusion. For a basic introduction to sets see the article on sets, for a fuller account see naive set theory, and for a full rigorous axiomatic treatment see axiomatic set theory.
Set theory is the branch of mathematical logic that studies sets, ... For example, the intersection of {1, 2, 3} and {2, 3, 4} is the set {2, 3}.
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
A Sperner family is a set family in which none of the sets contains any of the others. Sperner's theorem bounds the maximum size of a Sperner family. A Helly family is a set family such that any minimal subfamily with empty intersection has bounded size. Helly's theorem states that convex sets in Euclidean spaces of bounded dimension form Helly ...
In lattice theory, the operation that combines two elements to produce their greatest lower bound, analogous to intersection in set theory. member An individual element of a set. membership The relation between an element and a set in which the element is included within the set. mice Plural of mouse Milner–Rado paradox
For more about elementary set theory, see set, set theory, algebra of sets, and naive set theory. For an introduction to set theory at a higher level, see also axiomatic set theory, cardinal number, ordinal number, Cantor–Bernstein–Schroeder theorem, Cantor's diagonal argument, Cantor's first uncountability proof, Cantor's theorem, well ...
A well-working machinery of intersecting algebraic cycles V and W requires more than taking just the set-theoretic intersection V ∩ W of the cycles in question. If the two cycles are in "good position" then the intersection product, denoted V · W, should consist of the set-theoretic intersection of the two subvarieties. However cycles may be ...