Strategy dynamics: Difference between revisions

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{{For|other uses|Successor (disambiguation){{!}}Successor}}
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{{Unreferenced|date=June 2012}}
In [[mathematics]], the '''successor function''' or '''successor operation''' is a [[primitive recursive function]] defined by
 
:<math>S(n)=n+1. \, </math>
 
We have ''S''(1) = 1 + 1 = 2, ''S''(''S''(1)) = 2 + 1 = 3, ...
 
The successor function is used in the [[Peano axioms]] which define the [[natural number]]s. 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:
 
:<math>m+0=m</math>
:<math>m+S(n)=S(m)+n</math>
 
This yields 5 + 2 = 5 + ''S''(1) = ''S''(5) + 1 = 6 + 1 = 6 + ''S''(0) = ''S''(6) + 0 = 7 + 0 = 7
 
It is also one of the primitive functions used in the characterization of computability by [[computable function|recursive function]]s.
 
==See also==
*[[successor ordinal]]
*[[successor cardinal]]
*[[Increment]]
 
[[Category:Mathematical logic]]
[[Category:Arithmetic]]
[[Category:Logic in computer science]]
 
 
{{mathlogic-stub}}

Latest revision as of 16:13, 4 September 2014

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