Omega

For other uses, see Omega (disambiguation).

Greek alphabet
Αα	Alpha	Νν	Nu
Ββ	Beta	Ξξ	Xi
Γγ	Gamma	Οο	Omicron
Δδ	Delta	Ππ	Pi
Εε	Epsilon	Ρρ	Rho
Ζζ	Zeta	Σσς	Sigma
Ηη	Eta	Ττ	Tau
Θθ	Theta	Υυ	Upsilon
Ιι	Iota	Φφ	Phi
Κκ	Kappa	Χχ	Chi
Λλ	Lambda	Ψψ	Psi
Μμ	Mu	Ωω	Omega
History
Archaic local variants  ·  ·  ·  ·  ·
Ligatures (ϛ, ȣ, ϗ) · Diacritics
Numerals: (6) · (90) · (900)
In other languages
Bactrian  · Coptic  · Albanian
Scientific symbols
Book  · Category · Commons

Omega (majuscule: Ω, minuscule: ω; Greek Ωμέγα) is the 24th and last letter of the Greek alphabet. In the Greek numeric system, it has a value of 800. The word literally means "great O" (ō mega, mega meaning 'great'), as opposed to omicron, which means "little O" (o mikron, micron meaning "little"). This name is Byzantine; in Classical Greek, the letter was called ō (ὦ), whereas the omicron was called ou (οὖ). The form of the uppercase letter derives from that of an omicron (Ο) broken up at the side (), with the edges subsequently turned outwards (, , ). The modern lowercase shape goes back to the uncial form , a form that developed during the 3rd century BC in ancient handwriting on papyrus, from a flattened-out form of the letter () that had its edges curved even further upwards.

Phonetically, the Ancient Greek Ω is a long open-mid o [ɔː], equal to the vowel of British English raw. In Modern Greek Ω represents the same sound as omicron. The letter omega is transcribed ō or simply o.

Omega (the last letter of the Greek alphabet) is often used to denote the last, the end, or the ultimate limit of a set, in contrast to alpha, the first letter of the Greek alphabet. In the New Testament book of Revelation, God is declared to be the "alpha and omega, the beginning and the end, the first and the last".

Omega was also adopted into the early Cyrillic alphabet. See Cyrillic omega (Ѡ, ѡ). A Raetic variant is conjectured to be at the origin or parallel evolution of the Elder Futhark ᛟ.

Omega was also adopted into the Latin alphabet, as a letter of the 1982 revision to the African reference alphabet. It has had little use. See Latin omega.

The symbol Ω (majuscule letter)

The majuscule letter Ω is used as a symbol:

• 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 only included for backwards compatibility and the Greek uppercase omega character (U+03A9, Ω) is preferred.
  • 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 / computer science:
  • in notation related to Big O notation to describe the asymptotic behavior of functions.
  • Chaitin's constant.
• In mathematics
  • In complex analysis, the Omega constant, a solution of Lambert's W function
  • A variable for a 2-dimensional region in calculus, usually corresponding to the domain of a double integral.
  • In set theory, the first uncountable ordinal number (more commonly written as ω₁)
  • 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 statistics, it is used as the symbol for the sample space, or total set of possible outcomes.
  • In physics, it is used to represent angular frequency
• As part of logo or trademark:
  • The logo of Omega Watches SA.
  • 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.

• Other
  • The symbol of the resistance movement against the Vietnam-era draft
  • Year or date of death
  • Used to refer to the lowest-ranked wolf in a pack

The symbol ω (minuscule letter)

The minuscule letter ω is used as a symbol:

• 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 genomics, as a measure of evolution at the protein level (also denoted as d_N/d_S or K_a/K_s ratio).
• Physics:
  • angular velocity or angular frequency
  • Computational fluid dynamics: the specific turbulence dissipation rate
  • 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
  • In astronomy (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 ω₀)
  • The complex cube roots of 1
  • The Wright Omega function
  • A generic differential form
  • 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