Definition: Set of Natural Numbers (Peano)deleteeditadd to favorites[id:664]vote: last edited 1 week ago by bookofproofs Notation show notationA set \(N\) fulfilling the Peano axioms is called the set of natural numbers. The set is well-defined, which follows from the extensionality principle, since all sets fulfilling these axioms can be considered as the same. We denote this set as \[\mathbb N:=\{0,1,2,3,\ldots\}.\] Further Reading [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 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 Corollary add add a new Algorithm add add a new Bibliography (Branch) add add a new Definition add add a new Comment (Branch) add |
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The contents of book of proofs are licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License.