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Finite set

In mathematics, a finite set is a collection of finitely many different things; the things are called elements or members of the set and are typically mathematical objects, such as numbers, symbols, points in space, lines, other geometric shapes, variables, or other sets.

Necessary and sufficient conditions for finiteness, Basic properties & Definition and terminology

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Necessary and sufficient conditions for finiteness

Kazimierz KuratowskiPaul StäckelTotal orderingWell-orderedOnto
20 related topics

Basic properties

Proper subsetDedekind-finiteZFCSet theoryProved
15 related topics

Definition and terminology

Peano axiomsVon Neumann ordinalsBijectionEmptyVacuously
9 related topics

Overview

MathematicsElementsMathematical objectsGeometric shapesNatural number
13 related topics

Topics to explore

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Overview

Definition and terminology

Basic properties

Necessary and sufficient conditions for finiteness

Uniqueness of cardinality

Advanced semantic analysis

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Map overview Semantic statistics

Finite set

Nodes65
Edges64
Triples42
Avg. degree1.97
Density0.030769
Components1

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Finite set

Top relations

related to Necessary and sufficient conditions for finiteness · 11
Finite set → Alfred Tarski, Dedekind-finite, Equivalently, Every, Fraenkel, In, In Zermelo, Kazimierz Kuratowski, Paul Stäckel, That, ZF
related to Basic properties · 10
Finite set → Any, As, Dedekind-finite, Fraenkel, Similarly, The, Using, Zermelo, ZF, ZFC
related to Uniqueness of cardinality · 8
Finite set → An, Analysis, However, If, Intuitively, Lemma, Terence Tao, The
related to Definition and terminology · 7
Finite set → For, If, In, Peano, The, Then, Von Neumann
is a · 3
Finite set → collection of finitely many different things, natural number, set of its non-empty subsets
related to External links · 3
Finite set → Barile, Margherita, MathWorld

Important terminology Word statistics

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Important terminology

displaystyle set finite cardinality sets elements every also called function choice axiom element cannot number mathematical bijection empty subset theory

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Finite setis acollection of finitely many different things0.90text
Finite setis anatural number0.90text
Finite setis aset of its non-empty subsets0.90text
Finite setrelated to Basic propertiesAny0.60section
Finite setrelated to Basic propertiesAs0.60section
Finite setrelated to Basic propertiesDedekind-finite0.60section
Finite setrelated to Basic propertiesUsing0.60section
Finite setrelated to Basic propertiesZFC0.60section
Finite setrelated to Basic propertiesZF0.60section
Finite setrelated to Basic propertiesZermelo0.60section
Finite setrelated to Basic propertiesFraenkel0.60section
Finite setrelated to Basic propertiesThe0.60section

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