Common
Successor function
Elementary operation on a natural number
Successor function
In mathematics, the successor function or successor operation sends a natural number to the next one. The successor function is denoted by S {\displaystyle S} , so S ( n ) = n + 1 {\displaystyle S(n)=n+1} . For example, S ( 1 ) = 2 {\displaystyle S(1)=2} and S ( 2 ) = 3 {\displaystyle S(2)=3} . The successor function is one of the basic components used to build a primitive recursive function. Successor operations are also known as zeration in the context of a zeroth hyperoperation. In this context, the extension of zeration is addition, which is defined as repeated succession.
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