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Cartesian product

In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is an element of A and b is an element of B. In terms of set-builder notation, that is A × B = { ( a , b ) ∣ a ∈ A and b ∈ B } . {\displaystyle A\times B=\{(a,b)\mid a\in A\ {\mbox{ and }}\ b\in B\}.}

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Most common implementation (set theory)

ZFCPairingUnionPower setSpecification
16 related topics

Cartesian products of several sets

PlaneCartesian coordinate systemSingleton setEmpty functionCodomain
12 related topics

Examples

Standard 52-card deckStandard playing cardDisjointBijectionCartesian plane
7 related topics

Definitions outside set theory

Category theoryProductGraph theoryCartesian product of two graphsVertex
6 related topics

Topics to explore

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Overview

Set-theoretic definition

Examples

Most common implementation (set theory)

Cartesian products of several sets

Other forms

Definitions outside set theory

Advanced semantic analysis

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Map overview Semantic statistics

Cartesian product

Nodes61
Edges60
Triples89
Avg. degree1.97
Density0.032787
Components1

How this topic connects Entity context

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Cartesian product

Top relations

related to External links · 7
Cartesian product → Direct, Education Portal Academy, EMS Press, Encyclopedia, How, Mathematics, ProvenMath
related to Most common implementation (set theory) · 7
Cartesian product → Cartesian, Kuratowski's, Since, The, Therefore, Under, ZFC
related to Abbreviated form · 6
Cartesian product → Cartesian, If, X1, X2, X3, Xi
related to Cardinality · 6
Cartesian product → Both, Cartesian, For, That, The, Their Cartesian
related to Infinite Cartesian products · 6
Cartesian product → Cartesian, Even, For, If, It, Xi
related to Intersections, unions, complements and subsets · 6
Cartesian product → Cartesian, Let, Let Cartesian, The, Then, To
see also · 6
Cartesian product → Axiom, Cartesian, Cross, Direct, Product, SQL
related to A deck of cards · 5
Cartesian product → An, Ranks, Suits, The, The Cartesian
related to A two-dimensional coordinate system · 5
Cartesian product → Cartesian, In, René Descartes, The, Usually
related to Cartesian nth power · 5
Cartesian product → An, Cartesian, R2, The Cartesian, X2

Important terminology Word statistics

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Important terminology

product cartesian displaystyle set sets times ordered element functions defined example one power pairs definition infinite case called following theory

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cartesian productis aset of all infinite sequences with the i-th term in its corresponding set Xi0.90text
Cartesian productrelated to A deck of cardsAn0.60section
Cartesian productrelated to A deck of cardsThe0.60section
Cartesian productrelated to A deck of cardsThe Cartesian0.60section
Cartesian productrelated to A deck of cardsRanks0.60section
Cartesian productrelated to A deck of cardsSuits0.60section
Cartesian productrelated to A two-dimensional coordinate systemThe0.60section
Cartesian productrelated to A two-dimensional coordinate systemCartesian0.60section
Cartesian productrelated to A two-dimensional coordinate systemIn0.60section
Cartesian productrelated to A two-dimensional coordinate systemRené Descartes0.60section
Cartesian productrelated to A two-dimensional coordinate systemUsually0.60section
Cartesian productrelated to Abbreviated formIf0.60section

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