---
tag: YTERZRSVQ1
kind: concept
name: Omega
sources:
  - wikipedia: en:73634@r1376316324
    locator: Glossary of mathematical symbols, section Infinite numbers
    note: adopted
    mention: wikipedia://en/73634#TPN4
    sections: [Summary]
inventory: [JPK5ADFK6V]
---

## Summary

Denotes the first limit ordinal. It is also denoted $\omega_0$ and can be identified with the ordered set of the [[natural numbers|0MWKJ44V5A]].

With an [[ordinal|0RDJK7EQYY]] $i$ as a subscript, denotes the initial ordinal related to the $i$th aleph number.

In computer science, denotes the (unknown) greatest lower bound for the exponent of the computational complexity of [[matrix multiplication|032Q9FB8MT]].

Written as a [[function|0EPAT51DXQ]] of another function, it is used for comparing the asymptotic growth of two functions. See Big O notation § Related asymptotic notations.

In number theory, may denote the prime omega function. That is, $\omega(n)$ is the number of distinct prime factors of the integer $n$.