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Cardinal number

In mathematics, a cardinal number, or cardinal for short, is a kind of number that measures the cardinality of a set, i.e., how many elements there are in a set. The cardinal number associated with a set ⁠ A {\displaystyle A} ⁠ is generally denoted by ⁠ | A | {\displaystyle \vert A\vert } ⁠, with a vertical bar on each side, though it may also be denoted…

History, Constructive definition & Cardinal arithmetic

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Overview

Motivation

Cardinality function

Constructive definition

Cardinal comparison

Aleph numbers

Cardinal arithmetic

The continuum hypothesis

History

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Map overview Semantic statistics

Cardinal number

Nodes111
Edges110
Triples70
Avg. degree1.98
Density0.018018
Components1

How this topic connects Entity context

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Cardinal number

Top relations

related to Cardinal comparison · 11
Cardinal number → Any, Assuming, Bernstein, Dedekind, Dedekind-finite, Dedekind-infinite, Formally, It, Schroeder, The, The Cantor
related to Aleph numbers · 10
Cardinal number → Axiom, For, Hartogs's, Hebrew, If, Independence, Since, Such, The, They
related to Cardinality function · 9
Cardinal number → An, However, Hume's, If, It, Moschovakis, Specifically, The, Therefore
related to The continuum hypothesis · 9
Cardinal number → Both, CH, Fraenkel, GCH, In, Similarly, The, Zermelo, ZFC
related to history · 6
Cardinal number → Cantor, Each, Georg Cantor, He, The, Thus
related to Motivation · 5
Cardinal number → For, It, These, This, When
related to Von Neumann cardinal assignment · 5
Cardinal number → Neumann, The, This, Under, When
related to External links · 4
Cardinal number → Cardinal, EMS Press, Encyclopedia, Mathematics
related to Successor cardinal · 4
Cardinal number → For, Hartogs, If, Without
see also · 4
Cardinal number → Aleph, CountingInclusion, EnglishNominal, Mathematics

Important terminology Word statistics

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Important terminology

cardinal cardinality displaystyle set infinite numbers aleph number sets axiom choice theory finite cardinals also ordinal natural example mathematics bijection

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cardinal numberrelated to Aleph numbersThe0.60section
Cardinal numberrelated to Aleph numbersThey0.60section
Cardinal numberrelated to Aleph numbersHebrew0.60section
Cardinal numberrelated to Aleph numbersSince0.60section
Cardinal numberrelated to Aleph numbersFor0.60section
Cardinal numberrelated to Aleph numbersIf0.60section
Cardinal numberrelated to Aleph numbersAxiom0.60section
Cardinal numberrelated to Aleph numbersIndependence0.60section
Cardinal numberrelated to Aleph numbersSuch0.60section
Cardinal numberrelated to Aleph numbersHartogs's0.60section
Cardinal numberrelated to Cardinal arithmeticWe0.60section
Cardinal numberrelated to Cardinal arithmeticIt0.60section

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