Editing Axiom of extensionality (section)

{{short description|Axiom used in set theory}}
{{About|the axiom used in formal set theory|the article on ''extensionality'' in general|Extensionality}}

The '''axiom of extensionality''',<ref name=":0">{{Cite web |title=AxiomaticSetTheory |url=https://www.cs.yale.edu/homes/aspnes/pinewiki/AxiomaticSetTheory.html |access-date=2024-08-20 |website=www.cs.yale.edu}}</ref><ref>{{Cite web |title=Naive Set Theory |url=https://sites.pitt.edu/~jdnorton/teaching/paradox/chapters/sets/sets.html |access-date=2024-08-20 |website=sites.pitt.edu}}</ref> also called the '''axiom of extent''',<ref>{{Cite book |last=Bourbaki |first=N. |url=https://books.google.com/books?id=7eclBQAAQBAJ |title=Theory of Sets |date=2013-12-01 |publisher=Springer Science & Business Media |isbn=978-3-642-59309-3 |pages=67 |language=en}}</ref><ref>{{Cite book |last=Deskins |first=W. E. |url=https://books.google.com/books?id=2KrDAgAAQBAJ |title=Abstract Algebra |date=2012-05-24 |publisher=Courier Corporation |isbn=978-0-486-15846-4 |pages=2 |language=en}}</ref> is an [[axiom]] used in many forms of [[axiomatic set theory]], such as [[Zermelo–Fraenkel set theory]].<ref>{{Cite web |title=Zermelo-Fraenkel Set Theory |url=https://www.cs.odu.edu/~toida/nerzic/content/set/ZFC.html |access-date=2024-08-20 |website=www.cs.odu.edu}}</ref><ref>{{Cite web |title=Intro to Axiomatic (ZF) Set Theory |url=https://www.andrew.cmu.edu/user/kk3n/complearn/sets.html |access-date=2024-08-20 |website=www.andrew.cmu.edu}}</ref> The axiom defines what a [[Set (mathematics)|set]] is.<ref name=":0" /> Informally, the axiom means that the two [[set (mathematics)|set]]s ''A'' and ''B'' are equal [[if and only if]] ''A'' and ''B'' have the same members.