Omega

Omega (uppercase Ω, lowercase ω) is the twenty-fourth and final letter of the Greek alphabet. The name comes from o mega, meaning "great O," contrasted with omicron, meaning "small O." In science and mathematics, the symbol Omega or omega is used widely to denote a variety of ideas and quantities.

In set theory, ω denotes the first infinite ordinal, and ω1 denotes the first uncountable ordinal. In cosmology, Ω (uppercase) is the density parameter that expresses the ratio of the actual energy density to the critical density; the total Ω determines spatial curvature, with Ω ≈ 1 indicating a flat universe.

In physics and engineering, ω commonly denotes angular frequency or angular velocity, defined as the rate of rotation in radians per unit time. It is related to ordinary frequency f by ω = 2πf.

In computer science, Big-Omega (Ω) expresses a lower bound on a function's growth; little-omega (ω) denotes a lower bound that grows strictly faster than any constant multiple of the compared function for large inputs.

An independent mathematical constant named the Omega constant is defined as the value w satisfying w e^w = 1, namely w = W(1), and is approximately 0.567143. It appears in the study of certain transcendental equations involving exponentials.