---
tag: 0YSCSX5YZC
kind: concept
name: Ordinal number
aliases: [ordinal, von-neumann-ordinal]
msc: ["03E10"]
sources:
  - url: https://en.wikipedia.org/wiki/Ordinal_number
    locator: lead section
same_as:
  wikidata: Q191780
  wikipedia: Ordinal number
---

## Summary

Ordinal numbers extend the natural numbers to measure the length of well-ordered sets, including infinite ones.
Each well-ordered set is order isomorphic to exactly one ordinal.