History

The symbol Ω (uppercase letter)

• In chemistry: For oxygen-18, a natural, stable isotope of oxygen.^[5]

• In physics: For ohm – SI unit of electrical resistance; formerly also used upside down (℧) to represent mho, the old name for the inverse of an ohm (now siemens with symbol S) used for electrical conductance. Unicode has a separate code point for the ohm sign (U+2126, Ω), but it is included only for backward compatibility, and the Greek uppercase omega character (U+03A9, Ω) is preferred.^[6] In statistical mechanics, Ω refers to the multiplicity (number of microstates) in a system. The solid angle or the rate of precession in a gyroscope. In particle physics to represent the Omega baryons. In astronomy (cosmology), Ω refers to the density of the universe, also called the density parameter. In astronomy (orbital mechanics), Ω refers to the longitude of the ascending node of an orbit.

• In mathematics and computer science: In complex analysis, the Omega constant, a solution of Lambert's W function In differential geometry, the space of differential forms on a manifold (of a certain degree, usually with a superscript). A variable for a 2-dimensional region in calculus, usually corresponding to the domain of a double integral. In topos theory, the (codomain of the) subobject classifier of an elementary topos. In combinatory logic, the looping combinator, (λ x. x x) (λ x. x x) In group theory, the omega and agemo subgroups of a p-group, Ω(G) and ℧(G) In group theory, Cayley's Ω process as a partial differential operator. In statistics, it is used as the symbol for the sample space, or total set of possible outcomes. In number theory, Ω(n) is the number of prime divisors of n. In notation related to Big O notation to describe the asymptotic behavior of functions. Chaitin's constant.

• As part of logo or trademark: The logo of Omega Watches SA. Part of the original Pioneer logo. Part of the Badge of the Supreme Court of the United Kingdom. Part of the mission patch for STS-135, as it was the last mission of the Space Shuttle program. The logo of the God of War video game series based on Greek mythology. In God of War (2018), it is revealed it stands as the symbol of war in Greece. The logo of E-123 Omega, a Sonic the Hedgehog character. The logo of the Heroes of Olympus series, based on Greek mythology. the logo of the Ultramarines in Warhammer 40,000 The logo of Primal Groudon, the version mascot of Pokémon Omega Ruby. The logo of Darkseid in DC comics One of the logos of professional wrestler Kenny Omega

• Other The symbol of the resistance movement against the Vietnam-era draft in the United States Year or date of death Used to refer to the lowest-ranked wolf in a pack In eschatology, the symbol for the end of everything In molecular biology, the symbol is used as shorthand to signify a genetic construct introduced by a two-point crossover Omega Particle in the Star Trek universe The final form of NetNavi bosses in some of the Mega Man Battle Network games The personal symbol for Death, as worn by Death in the Discworld series by Terry Pratchett The symbol to represent Groudon in Pokémon Omega Ruby and Alpha Sapphire A secret boss in the Final Fantasy series called Omega ( Ω ) Weapon. A character from the series Doctor Who

The symbol ω (lower case letter)

• Biochemistry and chemistry: Denotes the carbon atom furthest from the carboxyl group of a fatty acid In biochemistry, for one of the RNA polymerase subunits In biochemistry, for the dihedral angle associated with the peptide group, involving the backbone atoms Cα-C'-N-Cα In biology, for the fitness. In genomics, as a measure of evolution at the protein level (also denoted as dN/dS or Ka/Ks ratio)

• Physics Angular velocity or angular frequency In computational fluid dynamics, the specific turbulence dissipation rate In meteorology, the change of pressure with respect to time of a parcel of air In circuit analysis and signal processing to represent natural frequency, related to frequency f by ω = 2πf In astronomy, as a ranking of a star's brightness within a constellation In orbital mechanics, as designation of the argument of periapsis of an orbit In particle physics to represent the omega meson

• Computer science: In notation related to Big O notation, the asymptotically dominant nature of functions In relational database theory to represent NULL, a missing or inapplicable value

• Mathematics: The first transfinite ordinal number, often identified with the set of natural numbers including 0 (sometimes written ) In set theory, the first uncountable ordinal number (more commonly written as ω1) A primitive root of unity, like the complex cube roots of 1 The Wright Omega function A generic differential form In number theory, ω(n) is the number of distinct prime divisors of n In number theory, an arithmetic function In combinatory logic, the self-application combinator, (λ x. x x) In mathematical/options finance, the elasticity of financial options In analytical investment management, the tracking error of an investment manager

• Other: Used in place of ん in Japanese typing shorthand. In linguistics, the phonological word In textual criticism, the archetype of a manuscript tradition In sociology, used to refer to the lowest ranking member of a group In shift_JIS art, used to represent the cat's mouth. (e.g. (´･ω･`) ｼｮﾎﾞｰﾝ)

Character encodings

Greek omega/Coptic oou

Cyrillic omega

Latin/IPA omega

Technical omega symbols

Mathematical omega

See also

• Alpha and Omega