Omega

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
Other characters
	Digamma		Stigma
	Heta		San
	Qoppa		Sampi
Greek diacritics

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").^[1] This name is Byzantine; in Classical Greek, the letter was called ō (ὦ), whereas the Omicron was called ou (οὖ).^[2] The form of the lowercase letter derives from a double omicron, which came to be written open at the top, whereas the uppercase derives from an underlined omicron, which came to be open at the bottom.

Phonetically, the Ancient Greek Ω is a long open-mid o [ɔː], equal to the vowel of 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".^[3]

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.

• In chemistry:
  • For Oxygen-18 a natural, stable isotope of oxygen
• 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.^[4]
  • For angular velocity in circular motion
  • 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 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.
• As part of logo or trademark:
  • The logo of Omega Watches SA.
  • Part of the Badge of the Supreme Court of the United Kingdom.

• In fictional worlds:
  • In the fictional world of Star Trek, the Omega symbol is used in conjunction with the Omega Directive.
  • As the logo of the popular PlayStation franchise God of War.
  • In the fictional universe Warhammer 40,000, the symbol for the Sons of Orar Chapter and, if turned upside down, the symbol for the Ultramarine Chapter of the Space Marines (Warhammer 40,000).
  • In the popular web series Red vs Blue the Blood Gulch Chronicles Omega (or O'Malley) is Freelancer Tex's AI implant and the main antagonist of the Blood Gulch Chronicles
  • In Locke and Key, the antagonist, Dodge, is searching for the Omega Key.
  • In the X-Men Movies the symbol is used in tattoos by mutants (particularly those who join the Brotherhood of Mutants) to publicly announce their mutant status.
  • In the Caprica television series, Tauron's use the symbol to represent marriage.
  • In the EarthBound video game series, Ω denotes the most powerful incarnation of a psychic attack.
  • In the Sonic the Hedgehog series there is a robot named E-123 Omega.

• Other
  • The Marilyn Manson album Mechanical Animals has false band within the album called Omēga and the Mechanical Animals
  • 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
  • Can be referred to the end of death or even time. The name of the end.
  • As a tattoo, to symbolise marriage in monogamy. The bottom of the symbol is sealed should the partner die.
  • Was part of the Pioneer Corporation's logo from 1970-1995.

The symbol Ω (lower case 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).
• 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
  • 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.
  • Also referred to as wubula by high school math teams in the US
• 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 particle physics to represent the omega meson
• 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 phonology, for a prosodic (or phonological) word.
  • In sociology, used to refer to the lowest ranking member of a group.

Notes

1. ↑ The Greek Alphabet
2. ↑ Herbert Weir Smyth. A Greek Grammar for Colleges. §1
3. ↑ Revelation 22:13, KJV, and see also 1:8, Greek ἐγὼ τὸ ἄλφα καὶ τὸ ὦ, ὁ πρῶτος καὶ ὁ ἔσχατος, ἡ ἀρχὴ καὶ τὸ τέλος. Or in Revelation 1:8 as seen in the Latin Vulgate Bible, the Greek is shown, surrounded by Latin: "ego sum α et ω principium et finis dicit Dominus Deus qui est et qui erat et qui venturus est Omnipotens"
4. ↑ Excerpts from The Unicode Standard, Version 4.0, accessed 11 October 2006