Omega

Summary

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

With an ordinal $i$ 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.

Written as a function 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 $n$.