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- Successor_function abstract "In mathematics, the successor function or successor operation is a primitive recursive function S such that S(n) = n+1 for each natural number n.For example, S(1) = 2 and S(2) = 3.The successor function is used in the Peano axioms which define the natural numbers. As such, it is not defined by addition, but rather is used to define all natural numbers beyond 0, as well as addition. For example, 1 is defined to be S(0), and addition on natural numbers is defined recursively by:This yields e.g. 5 + 2 = 5 + S(1) = S(5) + 1 = 6 + 1 = 6 + S(0) = S(6) + 0 = 7 + 0 = 7When natural numbers are constructed based on set theory, a common approach is to define the number 0 to be the empty set {}, and the successor S(x) to be x ∪ { x }. The axiom of infinity then guarantees the existence of a set ℕ that contains 0 and is closed with respect to S; members of ℕ are called natural numbers.The successor function is the level-0 foundation of the infinite hierarchy of hyperoperations (used to build addition, multiplication, exponentiation, tetration, etc.).It is also one of the primitive functions used in the characterization of computability by recursive functions.".
- Successor_function wikiPageID "325637".
- Successor_function wikiPageLength "1883".
- Successor_function wikiPageOutDegree "19".
- Successor_function wikiPageRevisionID "688757936".
- Successor_function wikiPageWikiLink Addition.
- Successor_function wikiPageWikiLink Axiom_of_infinity.
- Successor_function wikiPageWikiLink Category:Arithmetic.
- Successor_function wikiPageWikiLink Category:Logic_in_computer_science.
- Successor_function wikiPageWikiLink Category:Mathematical_logic.
- Successor_function wikiPageWikiLink Closure_(mathematics).
- Successor_function wikiPageWikiLink Computable_function.
- Successor_function wikiPageWikiLink Exponentiation.
- Successor_function wikiPageWikiLink Hyperoperation.
- Successor_function wikiPageWikiLink Mathematics.
- Successor_function wikiPageWikiLink Multiplication.
- Successor_function wikiPageWikiLink Natural_number.
- Successor_function wikiPageWikiLink Peano_axioms.
- Successor_function wikiPageWikiLink Primitive_recursive_function.
- Successor_function wikiPageWikiLink Successor_cardinal.
- Successor_function wikiPageWikiLink Successor_ordinal.
- Successor_function wikiPageWikiLink Tetration.
- Successor_function wikiPageWikiLinkText "Successor function".
- Successor_function wikiPageWikiLinkText "Successor".
- Successor_function wikiPageWikiLinkText "succession".
- Successor_function wikiPageWikiLinkText "successor function".
- Successor_function wikiPageWikiLinkText "successor operation".
- Successor_function wikiPageWikiLinkText "successor".
- Successor_function wikiPageWikiLinkText "successors".
- Successor_function wikiPageUsesTemplate Template:!.
- Successor_function wikiPageUsesTemplate Template:Cite_book.
- Successor_function wikiPageUsesTemplate Template:For.
- Successor_function wikiPageUsesTemplate Template:Mathlogic-stub.
- Successor_function wikiPageUsesTemplate Template:Reflist.
- Successor_function subject Category:Arithmetic.
- Successor_function subject Category:Logic_in_computer_science.
- Successor_function subject Category:Mathematical_logic.
- Successor_function hypernym S.
- Successor_function type Field.
- Successor_function comment "In mathematics, the successor function or successor operation is a primitive recursive function S such that S(n) = n+1 for each natural number n.For example, S(1) = 2 and S(2) = 3.The successor function is used in the Peano axioms which define the natural numbers. As such, it is not defined by addition, but rather is used to define all natural numbers beyond 0, as well as addition. For example, 1 is defined to be S(0), and addition on natural numbers is defined recursively by:This yields e.g.".
- Successor_function label "Successor function".
- Successor_function sameAs Q7632653.
- Successor_function sameAs Fonction_successeur.
- Successor_function sameAs m.0jwr5c6.
- Successor_function sameAs Q7632653.
- Successor_function wasDerivedFrom Successor_function?oldid=688757936.
- Successor_function isPrimaryTopicOf Successor_function.