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Intersection (set theory)

Index Intersection (set theory)

In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements. [1]

35 relations: Associative property, Axiom schema of replacement, Cardinality, Commutative property, Complement (set theory), De Morgan's laws, Empty set, Graduate Texts in Mathematics, Identity element, If and only if, Index set, Infinite product, Inhabited set, Intersection graph, Iterated binary operation, List of mathematical symbols, Logical conjunction, Mathematics, MinHash, Multiple (mathematics), Naive set theory, Natural number, Parity (mathematics), Power set, Prime number, Set (mathematics), Set theory, Set-builder notation, Sigma-algebra, Symmetric difference, Union (set theory), Universal quantification, Universal set, Vacuous truth, Zermelo–Fraenkel set theory.

Associative property

In mathematics, the associative property is a property of some binary operations.

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Axiom schema of replacement

In set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZF) that asserts that the image of any set under any definable mapping is also a set.

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In mathematics, the cardinality of a set is a measure of the "number of elements of the set".

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Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

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Complement (set theory)

In set theory, the complement of a set refers to elements not in.

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De Morgan's laws

In propositional logic and boolean algebra, De Morgan's laws are a pair of transformation rules that are both valid rules of inference.

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Empty set

In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.

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Graduate Texts in Mathematics

Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.

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Identity element

In mathematics, an identity element or neutral element is a special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them.

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If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

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Index set

In mathematics, an index set is a set whose members label (or index) members of another set.

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Infinite product

In mathematics, for a sequence of complex numbers a1, a2, a3,...

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Inhabited set

In constructive mathematics, a set A is inhabited if there exists an element a\in A. In classical mathematics, this is the same as the set being nonempty; however, this equivalence is not valid in intuitionistic logic.

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Intersection graph

In the mathematical area of graph theory, an intersection graph is a graph that represents the pattern of intersections of a family of sets.

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Iterated binary operation

In mathematics, an iterated binary operation is an extension of a binary operation on a set S to a function on finite sequences of elements of S through repeated application.

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List of mathematical symbols

This is a list of symbols used in all branches of mathematics to express a formula or to represent a constant.

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Logical conjunction

In logic, mathematics and linguistics, And (∧) is the truth-functional operator of logical conjunction; the and of a set of operands is true if and only if all of its operands are true.

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Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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In computer science and data mining, MinHash (or the min-wise independent permutations locality sensitive hashing scheme) is a technique for quickly estimating how similar two sets are.

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Multiple (mathematics)

In science, a multiple is the product of any quantity and an integer.

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Naive set theory

Naïve set theory is any of several theories of sets used in the discussion of the foundations of mathematics.

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Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

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Parity (mathematics)

In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd.

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Power set

In mathematics, the power set (or powerset) of any set is the set of all subsets of, including the empty set and itself, variously denoted as, 𝒫(), ℘() (using the "Weierstrass p"),,, or, identifying the powerset of with the set of all functions from to a given set of two elements,.

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Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

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Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

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Set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

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Set-builder notation

In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements or stating the properties that its members must satisfy.

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In mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a collection Σ of subsets of X that includes the empty subset, is closed under complement, and is closed under countable unions and countable intersections.

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Symmetric difference

In mathematics, the symmetric difference, also known as the disjunctive union, of two sets is the set of elements which are in either of the sets and not in their intersection.

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Union (set theory)

In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.

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Universal quantification

In predicate logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all".

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Universal set

In set theory, a universal set is a set which contains all objects, including itself.

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Vacuous truth

In mathematics and logic, a vacuous truth is a statement that asserts that all members of the empty set have a certain property.

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Zermelo–Fraenkel set theory

In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.

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Empty intersection, Intersect (set theory), Intersection (sets), Intersection set theory, Intersection sign, Nullary intersection, Set intersection, Set theoretic intersection, Set theory intersection, Set-theoretic intersection, , .


[1] https://en.wikipedia.org/wiki/Intersection_(set_theory)

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