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Ordered pair

In mathematics, an ordered pair, denoted (a, b), is a pair of objects in which their order is significant. If a and b are different, then (a,b) is different from (b,a). In contrast, the unordered pair {a,b} always equals the unordered pair {b,a}.

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Defining the ordered pair using set theory

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Ordered pair

Nodes58
Edges57
Triples58
Avg. degree1.97
Density0.034483
Components1

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Ordered pair

Top relations

related to Morse definition · 11
Ordered pair → Cartesian, He, Kelley, Kuratowski, Kuratowski's, Morse, Rosser, Similarly, The Kuratowski, The Quine, This
related to Quine–Rosser definition · 11
Ordered pair → Applying, As, By, Finally, Further, In, Let, Quine, Rosser, The, This
see also · 8
Ordered pair → Andrzej, Cartesian, Def5, Formalized Mathematics, Grothendieck, Grothendieck Set Theory, Journal, Tarski
related to Kuratowski's definition · 5
Ordered pair → Given, In, Kazimierz Kuratowski, The, When
related to Wiener's definition · 5
Ordered pair → He, Norbert Wiener, Principia Mathematica, Wiener, With
related to Cantor–Frege definition · 4
Ordered pair → Cantor, Early, Frege, This
related to Defining the ordered pair using set theory · 4
Ordered pair → Diepert, Hence, If, Several
related to Generalities · 4
Ordered pair → Cartesian, Let, The, Then
related to Category theory · 2
Ordered pair → In, While
related to Informal and formal definitions · 2
Ordered pair → In, This

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Important terminology

ordered pair set displaystyle definition pairs sets property theory defined first second objects characteristic called also elements kuratowski short one

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
the axiomatic set theory NFinstance ofIn type theory and in outgrowths thereof0.80text
the Quineinstance ofIn type theory and in outgrowths thereof0.80text
Ordered pairrelated to Cantor–Frege definitionEarly0.60section
Ordered pairrelated to Cantor–Frege definitionCantor0.60section
Ordered pairrelated to Cantor–Frege definitionFrege0.60section
Ordered pairrelated to Cantor–Frege definitionThis0.60section
Ordered pairrelated to Category theoryIn0.60section
Ordered pairrelated to Category theoryWhile0.60section
Ordered pairrelated to Defining the ordered pair using set theoryIf0.60section
Ordered pairrelated to Defining the ordered pair using set theoryHence0.60section
Ordered pairrelated to Defining the ordered pair using set theorySeveral0.60section
Ordered pairrelated to Defining the ordered pair using set theoryDiepert0.60section

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