Axiom: Axiom of Pairing (Ernst Zermelo 1908)deleteeditadd to favorites[id:667]vote: last edited 1 week ago by bookofproofs For any \(a,b\) there exist a set \(\{a,b\}\) containing both elements and nothing else. \[\forall a~\forall b~\exists X~\forall c~(c\in X\Leftrightarrow c=a\vee c=b)\] References [656] Hoffmann, Dirk W.: “Grenzen der Mathematik - Eine Reise durch die Kerngebiete der mathematischen Logik”, Spektrum Akademischer Verlag, 2011 What follows from what?This is (experimental) work in progress - if you miss an axiom, a definition, a theorem or a proof, if you find any inconsistencies you want to correct, or just know about a cool example or explanation you want to share with others, then join our team and help to improve this catalogue. Learn more about the axiomatic approach on BoP...Contribute to BoP: add a new Corollary add add a new Definition add add a new Motivation add add a new Example add add a new Application add add a new Explanation add add a new Interpretation add add a new Comment (Branch) add |
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