About: Set-theoretic definition of natural numbers

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In set theory, several ways have been proposed to construct the natural numbers. These include the representation via von Neumann ordinals, commonly employed in axiomatic set theory, and a system based on equinumerosity that was proposed by Gottlob Frege and by Bertrand Russell.

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rdf:type	Thing yago:WikicatBasicConceptsInInfiniteSetTheory yago:WikicatNumbers yago:Abstraction100002137 yago:Amount105107765 yago:Attribute100024264 yago:Cognition100023271 yago:Concept105835747 yago:Content105809192 yago:Explanation105793000 yago:HigherCognitiveProcess105770664 yago:Idea105833840 yago:Magnitude105090441 yago:Number105121418 yago:Process105701363 yago:Property104916342 yago:PsychologicalFeature100023100 yago:Theory105989479 yago:Thinking105770926 yago:WikicatFormalTheoriesOfArithmetic
rdfs:label	Von Neumanns Modell der natürlichen Zahlen (de) Construction des entiers naturels (fr) Set-theoretic definition of natural numbers (en) 自然数的集合论定义 (zh)
rdfs:comment	Il existe plusieurs méthodes classiques de construction des entiers naturels, mais on utilise aujourd’hui le plus souvent celle due à von Neumann . (fr) In set theory, several ways have been proposed to construct the natural numbers. These include the representation via von Neumann ordinals, commonly employed in axiomatic set theory, and a system based on equinumerosity that was proposed by Gottlob Frege and by Bertrand Russell. (en) 已经提出了多种使用集合论定义自然数的方式。 (zh)
rdfs:seeAlso	Zermelo ordinals
dcterms:subject	Basic concepts in infinite set theory
Wikipage page ID	428484 (xsd:integer)
Wikipage revision ID	1116636806 (xsd:integer)
Link from a Wikipage to another Wikipage	Proper class New Foundations Bertrand Russell Patrick Suppes Peano axioms Von Neumann ordinal One-to-one correspondence George Boolos Gottlob Frege Equinumerosity Equivalence class Stanford Encyclopedia of Philosophy Zermelo–Fraenkel set theory Empty set Successor function Axiomatic set theory Type theory Abraham Fraenkel Equivalence relation Cardinal number Basic concepts in infinite set theory Foundations of mathematics Natural deduction William S. Hatcher Chapman & Hall ZFC Axiom of infinity Hume's principle Natural number Category theory Recursively Set (mathematics) Set theory Russell paradox Edward Zalta Ackermann coding
Link from a Wikipage to an external page	https://randall-holmes.github.io/head.pdf http://plato.stanford.edu/entries/quine-nf https://randall-holmes.github.io/nf.html http://setis.library.usyd.edu.au/stanford/entries/settheory-alternative/ https://web.archive.org/web/*/http:/www.maths.may.ie/staff/gmg/nn.ps
sameAs	Set-theoretic definition of natural numbers Set-theoretic definition of natural numbers Set-theoretic definition of natural numbers Set-theoretic definition of natural numbers Set-theoretic definition of natural numbers Set-theoretic definition of natural numbers Set-theoretic definition of natural numbers Set-theoretic definition of natural numbers
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Harv dbt:Portal dbt:See_also dbt:Sfn
has abstract	Il existe plusieurs méthodes classiques de construction des entiers naturels, mais on utilise aujourd’hui le plus souvent celle due à von Neumann . (fr) In set theory, several ways have been proposed to construct the natural numbers. These include the representation via von Neumann ordinals, commonly employed in axiomatic set theory, and a system based on equinumerosity that was proposed by Gottlob Frege and by Bertrand Russell. (en) 已经提出了多种使用集合论定义自然数的方式。 (zh)
prov:wasDerivedFrom	wikipedia-en:Set-theoretic_definition_of_natural_numbers?oldid=1116636806&ns=0
page length (characters) of wiki page	5750 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Set-theoretic_definition_of_natural_numbers
is rdfs:seeAlso of	Ordinal number
is Link from a Wikipage to another Wikipage of	New Foundations Bertrand Russell Gottlob Frege Constructive set theory Epsilon-induction Computable set Empty set Successor function

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