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, so S(n) = n + 1. For example, S(1) = 2 and 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: H₀(a, b) = 1 + b. In this context, the extension of zeration is addition, which is defined as repeated succession.