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Intersection (set theory)

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]

For broader coverage of this topic, see Intersection (mathematics).

Type

Set operation

Set theory

The intersection of and is the set of elements that lie in both set and set .

Notation and terminology[edit]

Intersection is written using the symbol "" between the terms; that is, in infix notation. For example: The intersection of more than two sets (generalized intersection) can be written as: which is similar to capital-sigma notation.


For an explanation of the symbols used in this article, refer to the table of mathematical symbols.

The intersection of the sets {1, 2, 3} and {2, 3, 4} is {2, 3}.

The number 9 is not in the intersection of the set of {2, 3, 5, 7, 11, ...} and the set of odd numbers {1, 3, 5, 7, 9, 11, ...}, because 9 is not prime.

prime numbers

 – Identities and relationships involving sets

Algebra of sets

 – Definition of the number of elements in a set

Cardinality

 – Set of the elements not in a given subset

Complement

 – Shape formed from points common to other shapes

Intersection (Euclidean geometry)

 – Graph representing intersections between given sets

Intersection graph

 – Branch of algebraic geometry

Intersection theory

 – Equalities for combinations of sets

List of set identities and relations

 – Logical connective AND

Logical conjunction

 – Data mining technique

MinHash

 – Informal set theories

Naive set theory

 – Elements in exactly one of two sets

Symmetric difference

 – Set of elements in any of some sets

Union

(1993). The Joy of Sets: Fundamentals of Contemporary Set Theory (Second ed.). New York, NY: Springer-Verlag. ISBN 3-540-94094-4.

Devlin, K. J.

(2000). "Set Theory and Logic". Topology (Second ed.). Upper Saddle River: Prentice Hall. ISBN 0-13-181629-2.

Munkres, James R.

Rosen, Kenneth (2007). "Basic Structures: Sets, Functions, Sequences, and Sums". Discrete Mathematics and Its Applications (Sixth ed.). Boston: McGraw-Hill.  978-0-07-322972-0.

ISBN

"Intersection". MathWorld.

Weisstein, Eric W.