Axiom of infinity
In axiomatic set theory and the branches of mathematics and philosophy that use it, the axiom of infinity is one of the axioms of Zermelo–Fraenkel set theory. It guarantees the existence of at least one infinite set, namely a set containing the natural numbers. It was first published by Ernst Zermelo as part of his set theory in 1908.
Actual infinityAlternative set theoryAxiom of InfinityAxiom of empty setAxiom of limitation of sizeAxiom of pairingAxiom of regularityAxiom schema of replacementBachmann–Howard ordinalConstructible universeConstructive proofConstructive set theoryControversy over Cantor's theoryEmpty setEquinumerosityExistence theoremFinite setGeneral set theoryGlossary of set theoryHereditarily countable setHereditarily finite setImplementation of mathematics in set theoryIndex of philosophy articles (A–C)Inductive set (axiom of infinity)Infinite setInfinityKripke–Platek set theoryList of axiomsMorse–Kelley set theoryNatural numberNew FoundationsOrdered pairOrdinal analysisParadoxes of set theoryParadoxical setPaul CohenPeano axiomsPositive set theoryPrincipia MathematicaQuasi-set theory
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Axiom of infinity
In axiomatic set theory and the branches of mathematics and philosophy that use it, the axiom of infinity is one of the axioms of Zermelo–Fraenkel set theory. It guarantees the existence of at least one infinite set, namely a set containing the natural numbers. It was first published by Ernst Zermelo as part of his set theory in 1908.
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Aksjomat nieskończoności – jed ...... nazywamy zbiorem induktywnym.
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Das Unendlichkeitsaxiom ist ei ...... g modifizierter Form übernahm.
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En mathématiques, dans le doma ...... e de celle exposée ci-dessous.
@fr
En teoria de conjunts, l'axiom ...... un nombre infinit d'elements.
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En teoría de conjuntos, el axi ...... número infinito de elementos.
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In axiomatic set theory and th ...... art of his set theory in 1908.
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In de axiomatische verzameling ...... van alle natuurlijk getallen.
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Na teoria dos conjuntos, o Axi ...... seu, tem outro elemento maior.
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Nella teoria degli insiemi, l' ...... di von Neumann-Bernays-Gödel.
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Oändlighetsaxiomet (infinitets ...... mängden uppräkneligt oändlig.
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Aksjomat nieskończoności – jed ...... nazywamy zbiorem induktywnym.
@pl
Das Unendlichkeitsaxiom ist ei ...... g modifizierter Form übernahm.
@de
En mathématiques, dans le doma ...... e de celle exposée ci-dessous.
@fr
En teoria de conjunts, l'axiom ...... un nombre infinit d'elements.
@ca
En teoría de conjuntos, el axi ...... número infinito de elementos.
@es
In axiomatic set theory and th ...... art of his set theory in 1908.
@en
In de axiomatische verzameling ...... van alle natuurlijk getallen.
@nl
Na teoria dos conjuntos, o Axi ...... seu, tem outro elemento maior.
@pt
Nella teoria degli insiemi, l' ...... = 1 ∪ {1} = {0} ∪ {1} = {0,1},
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Oändlighetsaxiomet (infinitets ...... mängden uppräkneligt oändlig.
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Aksiomo de senfineco
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Aksjomat nieskończoności
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Assioma dell'infinito
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Axiom of infinity
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Axioma de l'infinit
@ca
Axioma del infinito
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Axioma do infinito
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Axiome de l'infini
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Oneindigheidsaxioma
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Oändlighetsaxiomet
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