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



History  
Use in other languages  
Related topics  
 
Omega (capital: Ω, lowercase: 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]}
In phonetic terms, the Ancient Greek Ω is a long openmid o [ɔː], comparable to the vowel of British English raw. In Modern Greek, Ω represents the mid back rounded vowel /o/, the same sound as omicron. The letter omega is transcribed ō or simply o.
As the last letter of the Greek alphabet, Omega 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. Omega is also used in Christianity, as a part of the Alpha and Omega metaphor.
History
Ω was not part of the early (8th century BC) Greek alphabets. It was introduced in the late 7th century BC in the Ionian cities of Asia Minor to denote the long halfopen [ɔː]. It is a variant of omicron (Ο), broken up at the side (), with the edges subsequently turned outward (, , , ).^{[2]} The Dorian city of Knidos as well as a few Aegean islands, namely Paros, Thasos and Melos, chose the exact opposite innovation, using a brokenup circle for the short and a closed circle for the long /o/.^{[2]}
The name Ωμέγα is Byzantine; in Classical Greek, the letter was called ō (ὦ), whereas the omicron was called ou (οὖ).^{[3]} 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 flattenedout form of the letter () that had its edges curved even further upward.^{[4]}
In addition to the Greek alphabet, 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 (uppercase letter)
The uppercase letter Ω is used as a symbol:
 In chemistry:
 For oxygen18, 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 supersrcipt).
 A variable for a 2dimensional 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 pgroup, 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 Badge of the Supreme Court of the United Kingdom.
 Part of the mission patch for STS135, 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.
 The logo of E123 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
 Other
 The symbol of the resistance movement against the Vietnamera draft in the United States
 Year or date of death
 Used to refer to the lowestranked 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 twopoint crossover
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 CαC'NCα
 In biology, for the fitness.
 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
 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 ω_{1})
 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 selfapplication 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
Character  Ω  ω  Ⲱ  ⲱ  

Unicode name  GREEK CAPITAL LETTER OMEGA  GREEK SMALL LETTER OMEGA  COPTIC CAPITAL LETTER OOU  COPTIC SMALL LETTER OOU  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  937  U+03A9  969  U+03C9  11440  U+2CB0  11441  U+2CB1 
UTF8  206 169  CE A9  207 137  CF 89  226 178 176  E2 B2 B0  226 178 177  E2 B2 B1 
Numeric character reference  Ω  Ω  ω  ω  Ⲱ  Ⲱ  ⲱ  ⲱ 
Named character reference  Ω  ω  
DOS Greek  151  97  224  E0  
DOS Greek2  213  D5  250  FA  
Windows 1253  217  D9  249  F9  
TeX  \Omega  \omega 
^{[7]}
Cyrillic omega
Character  Ѡ  ѡ  ꙻ  

Unicode name  CYRILLIC CAPITAL LETTER OMEGA  CYRILLIC SMALL LETTER OMEGA  COMBINING CYRILLIC LETTER OMEGA  
Encodings  decimal  hex  decimal  hex  decimal  hex 
Unicode  1120  U+0460  1121  U+0461  42619  U+A67B 
UTF8  209 160  D1 A0  209 161  D1 A1  234 153 187  EA 99 BB 
Numeric character reference  Ѡ  Ѡ  ѡ  ѡ  ꙻ  ꙻ 
Character  Ѻ  ѻ  Ꙍ  ꙍ  

Unicode name  CYRILLIC CAPITAL LETTER ROUND OMEGA  CYRILLIC SMALL LETTER ROUND OMEGA  CYRILLIC CAPITAL LETTER BROAD OMEGA  CYRILLIC SMALL LETTER BROAD OMEGA  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  1146  U+047A  1147  U+047B  42572  U+A64C  42573  U+A64D 
UTF8  209 186  D1 BA  209 187  D1 BB  234 153 140  EA 99 8C  234 153 141  EA 99 8D 
Numeric character reference  Ѻ  Ѻ  ѻ  ѻ  Ꙍ  Ꙍ  ꙍ  ꙍ 
Latin/IPA omega
Character  ɷ  Ꞷ  ꞷ  

Unicode name  LATIN SMALL LETTER CLOSED OMEGA  LATIN CAPITAL LETTER OMEGA  LATIN SMALL LETTER OMEGA  
Encodings  decimal  hex  decimal  hex  decimal  hex 
Unicode  631  U+0277  42934  U+A7B6  42935  U+A7B7 
UTF8  201 183  C9 B7  234 158 182  EA 9E B6  234 158 183  EA 9E B7 
Numeric character reference  ɷ  ɷ  Ꞷ  Ꞷ  ꞷ  ꞷ 
Technical omega symbols
Character  ⍵  ⍹  Ω  ℧  

Unicode name  APL FUNCTIONAL SYMBOL OMEGA  APL FUNCTIONAL SYMBOL OMEGA UNDERBAR  OHM SIGN  INVERTED OHM SIGN  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  9077  U+2375  9081  U+2379  8486  U+2126  8487  U+2127 
UTF8  226 141 181  E2 8D B5  226 141 185  E2 8D B9  226 132 166  E2 84 A6  226 132 167  E2 84 A7 
Numeric character reference  ⍵  ⍵  ⍹  ⍹  Ω  Ω  ℧  ℧ 
Mathematical omega
Character  𝛀  𝛚  𝛺  𝜔  𝜴  𝝎  

Unicode name  MATHEMATICAL BOLD CAPITAL OMEGA  MATHEMATICAL BOLD SMALL OMEGA  MATHEMATICAL ITALIC CAPITAL OMEGA  MATHEMATICAL ITALIC SMALL OMEGA  MATHEMATICAL BOLD ITALIC CAPITAL OMEGA  MATHEMATICAL BOLD ITALIC SMALL OMEGA  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  120512  U+1D6C0  120538  U+1D6DA  120570  U+1D6FA  120596  U+1D714  120628  U+1D734  120654  U+1D74E 
UTF8  240 157 155 128  F0 9D 9B 80  240 157 155 154  F0 9D 9B 9A  240 157 155 186  F0 9D 9B BA  240 157 156 148  F0 9D 9C 94  240 157 156 180  F0 9D 9C B4  240 157 157 142  F0 9D 9D 8E 
UTF16  55349 57024  D835 DEC0  55349 57050  D835 DEDA  55349 57082  D835 DEFA  55349 57108  D835 DF14  55349 57140  D835 DF34  55349 57166  D835 DF4E 
Numeric character reference  𝛀  𝛀  𝛚  𝛚  𝛺  𝛺  𝜔  𝜔  𝜴  𝜴  𝝎  𝝎 
Character  𝝮  𝞈  𝞨  𝟂  𝟔  

Unicode name  MATHEMATICAL SANSSERIF BOLD CAPITAL OMEGA  MATHEMATICAL SANSSERIF BOLD SMALL OMEGA  MATHEMATICAL SANSSERIF BOLD ITALIC CAPITAL OMEGA  MATHEMATICAL SANSSERIF BOLD ITALIC SMALL OMEGA  MATHEMATICAL SANSSERIF BOLD ITALIC P.OOO OMEGA  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  120686  U+1D76E  120712  U+1D788  120744  U+1D7A8  120770  U+1D7C2  120788  U+1D7D4 
UTF8  240 157 157 174  F0 9D 9D AE  240 157 158 136  F0 9D 9E 88  240 157 158 168  F0 9D 9E A8  240 157 159 130  F0 9D 9F 82  240 157 159 148  F0 9D 9F 94 
UTF16  55349 57198  D835 DF6E  55349 57224  D835 DF88  55349 57256  D835 DFA8  55349 57282  D835 DFC2  55349 57300  D835 DFD4 
Numeric character reference  𝝮  𝝮  𝞈  𝞈  𝞨  𝞨  𝟂  𝟂  𝟔  𝟔 
These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.
Notes
 ↑ The Greek Alphabet
 1 2 Anne Jeffery (1961), The local scripts of archaic Greece, p.37–38.
 ↑ Herbert Weir Smyth. A Greek Grammar for Colleges. §1
 ↑ Edward M. Thompson (1912), Introduction to Greek and Latin paleography, Oxford: Clarendon. p.144
 ↑ http://www.cedex.es/NR/rdonlyres/B8A9522A5D6F4675921A24BB8458187B/124720/Capilla_et_al_geoENV_2012_Valencia_Espa%C3%B1a_Extended.pdf
 ↑ Excerpts from The Unicode Standard, Version 4.0. Retrieved 11 October 2006.
 ↑ Unicode Code Charts: Greek and Coptic (Range: 037003FF)