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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 requires 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, etc.).It is also one of the primitive functions used in the characterization of computability by recursive functions.".
- Successor_function wikiPageID "325637".
- Successor_function wikiPageRevisionID "599700217".
- Successor_function hasPhotoCollection Successor_function.
- Successor_function subject Category:Arithmetic.
- Successor_function subject Category:Logic_in_computer_science.
- Successor_function subject Category:Mathematical_logic.
- 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 m.0jwr5c6.
- Successor_function sameAs Q7632653.
- Successor_function sameAs Q7632653.
- Successor_function wasDerivedFrom Successor_function?oldid=599700217.
- Successor_function isPrimaryTopicOf Successor_function.