---
tag: 0AK9TGSNXY
kind: concept
name: Successor function
msc: [03F30]
sources:
  - url: https://en.wikipedia.org/wiki/Successor_function
    locator: lead section
same_as:
  wikidata: Q7632653
  wikipedia: Successor function
---

## Summary

The successor function is the function $S \colon \mathbb{N} \to \mathbb{N}$ that sends each natural number $n$ to the next natural number, $S(n) = n + 1$.
It is a primitive notion of the [[Peano axioms|0QFT7Z76N5]].