Successor function

In mathematics, the successor function or successor operation sends a natural number to the next one. The successor function is denoted by ${\displaystyle S}$, so ${\displaystyle S(n)=n+1}$. For example, ${\displaystyle S(1)=2}$ and ${\displaystyle S(2)=3}$. 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.