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Cardinality

In mathematics, cardinality is an inherent property of sets, roughly meaning the number of individual objects they contain, which may be infinite. The concept is understood through one-to-one correspondences between sets. That is, if their objects can be paired such that each object has a pair, and no object is paired more than once.

History, Countability & Cardinal numbers

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Overview

Basics

Comparing sets

Countability

Cardinal numbers

Cardinality of the continuum

Alternative and additional axioms

Skolem's paradox

History

Advanced semantic analysis

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Map overview Semantic statistics

Cardinality

Nodes300
Edges299
Triples178
Avg. degree1.99
Density0.006667
Components1

How this topic connects Entity context

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Cardinality

Top relations

related to Pre-Cantorian set theory · 15
Cardinality → David Hume, Galileo, Galileo Galilei, Galileo's, Gottlob Frege, However, Human Nature, Hume's, In, It, Moreover, Therefore, Treatise, Two New Sciences, When
related to Skolem's paradox · 15
Cardinality → Applied, But, Ernst Zermelo, Fraenkel, He, In, It, Löwenheim, Skolem, Skolem's, This, Thoralf Skolem, Thus, Zermelo, ZFC
related to Finite cardinals · 14
Cardinality → Combinatorics, Finite, For, Given, Hume's, In, It, Its, Other, Peano, Showing, The, This, Uniqueness
related to Without the axiom of choice · 14
Cardinality → AC, Assuming AC, Both, Choice, For, However, Informally, It, Similarly, Specifically, The, The Axiom, Thus, Whereas
related to Countable sets · 13
Cardinality → Bernstein, Calkin, For, However, Pre-Cantorian, Schröder, Similarly, So, The, Then, These, This, Wilf
related to Determinacy · 13
Cardinality → AC, AD, Banach, Despite, Determinacy, Existence, However, Lebesgue, Similarly, Tarski, The, The Axiom, Under AD
related to Alternative and additional axioms · 12
Cardinality → Around, Axiom, Axiomatic, Choice, Fraenkel, In, Infinity, Similarly, The, Thus, Zermelo, ZFC
related to Cardinality of the continuum · 12
Cardinality → Ancient, Cantor, Cauchy, Dedekind, First, For, Further, However, Reinterpreting, The, The Cantor, There
related to Etymology and related terms · 11
Cardinality → Around, Cantor, English, Georg Cantor, German, In, Jakob Steiner, Latin, Mächtigkeit, The, This
related to Inequality · 10
Cardinality → Antisymmetry, Bernstein, Cardinal, For, If, One, Schröder, That, The, This

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Important terminology

displaystyle set sets numbers number cardinal theory infinite one natural aleph mathbb function example finite vert called two real since

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cardinalityis ainherent property of sets0.90text
Zermeloinstance ofwhich has been shown to be both unprovable and undisprovable in standard set theories0.80text
unionsinstance ofa cardinal that cannot be approached from below using basic set-theoretic operations0.80text
limitsinstance ofa cardinal that cannot be approached from below using basic set-theoretic operations0.80text
and powersetsinstance ofa cardinal that cannot be approached from below using basic set-theoretic operations0.80text
Donald Ainstance ofits relationship with large cardinals and the continuum hypothesis is still of heavy interest among set theorists0.80text
the pairing between the intervalsinstance ofHe discussed examples0.80text
Paul Mahloinstance ofThis work was continued and popularized by several other influential set theorists0.80text
Cardinalityrelated to Aleph numbersThe0.60section
Cardinalityrelated to Aleph numbersHebrew0.60section
Cardinalityrelated to Aleph numbersThen0.60section
Cardinalityrelated to Aleph numbersVon Neumann0.60section

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