---
tag: Z92S2GVCX9
kind: concept
name: First uncountable ordinal
aliases: [least-uncountable-ordinal, minimal-uncountable-well-ordered-set, omega-one, omega-1, smallest-uncountable-ordinal, "1"]
sources:
  - wikipedia: en:20860540@r1371088292
    locator: First uncountable ordinal
    note: adopted
    mention: wikipedia://en/20860540
    sections: [Summary]
same_as:
  wikidata: Q3401770
  wikipedia: First uncountable ordinal
inventory: [NMDGMP121J]
---

## Summary

In mathematics, the **first uncountable ordinal**, traditionally denoted by $\omega_1$ or sometimes by $\Omega$, is the smallest [[ordinal number|0RDJK7EQYY]] that is the order type of an uncountable well-ordered set. It is the supremum (least upper bound) of all countable ordinals. In the von Neumann representation, the elements of $\omega_1$ are the countable ordinals (including finite ordinals), of which there are uncountably many.