omega

Look up Ω or ω in Wiktionary, the free dictionary.

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
Obsolete letters
	Digamma		Qoppa
	San		Sampi
Other characters
	Stigma		Sho
	Heta
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.

Phonetically, the Ancient Greek Ω is a long open-mid o [ɔː], similar to the vowel of English raw as pronounced in London or New York. 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, Christ is declared to be the "alpha and omega, the beginning and the end, the first and the last".^[3]

As the symbol of the Sumerian goddess Ninhursag, the omega has been depicted in art from around 3000 BC, though more generally from the early second millennium. It appears on some boundary stones on the upper tier, which indicates her importance.

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.

The symbol Ω (majuscule letter)

This section needs additional citations for verification. Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (August 2009)

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. ^[4]
  • For angular velocity in circular motion
  • 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.
  • The logo of the popular PlayStation franchise God of War.
  • As the symbol for the Sons of Orar Chapter and ,if turned upside down, the symbol for the Ultramarine Chapter both of the Space Marines (Warhammer 40,000) , in the fictional universe Warhammer 40,000

• Other
  • The symbol of the resistance movement against the Vietnam-era draft
  • Year or date of death

The symbol ω (lower case letter)

The minuscule letter ω is used as a symbol:

• Biochemisty 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 finance, the elasticity of financial options.
• 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 The Unicode Standard, Version 4.0, accessed 11 October 2006