# Omega

Omega /ˈmɪɡə, ˈmɛɡə/[1] (capital: Ω, lowercase: ω; Ancient Greek ὦ, later ὦ μέγα, Modern Greek ωμέγα) is the 24th and final letter in the Greek alphabet. In the Greek numeric system/Isopsephy (Gematria), it has a value of 800. The word literally means "great O" (ō mega, mega meaning "great"), as opposed to Ο ο omicron, which means "little O" (o mikron, micron meaning "little").[2]

In phonetic terms, the Ancient Greek Ω is a long open-mid o [ɔː], comparable to the vowel of English raw. In Modern Greek, Ω represents the mid back rounded vowel /o̞/, the same sound as omicron. The letter omega is transcribed ō or simply o.

As the final letter in 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; see Alpha and Omega.

## 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 a long open-mid back rounded vowel [ɔː]. It is a variant of omicron (Ο), broken up at the side (), with the edges subsequently turned outward (, , , ).[3] The Dorian city of Knidos as well as a few Aegean islands, namely Paros, Thasos and Melos, chose the exact opposite innovation, using a broken-up circle for the short and a closed circle for the long /o/.[3]

The name Ωμέγα is Byzantine; in Classical Greek, the letter was called ō (), whereas the omicron was called ou (οὖ).[4] 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 upward.[5]

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)

Plaque in Kos with "underlined O" form of omega.

The uppercase letter Ω is used as a symbol:

• In chemistry:
• For oxygen-18, a natural, stable isotope of oxygen.[6]
• 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.[7]
• 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, (S I I (S I I))
• 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 (counting multiplicity).[8]
• In notation related to Big O notation to describe the asymptotic behavior of functions.
• Chaitin's constant.
• In set theory, the first uncountable ordinal number (also sometimes written as ω1)
• 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
• The logo for Meow Wolf's Omega Mart in Area15, Las Vegas, Nevada.
• Other
• The symbol of the resistance movement against the Vietnam-era draft in the United States
• Year or date of death
• 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 called Omega, believed to be one of the creators of the Time Lords of Gallifrey.
• The symbol for the highest power level of a PSI attack in the MOTHER/EarthBound games

## The symbol ω (lower case letter)

The minuscule letter ω is used as a symbol:

• Biology, biochemistry and chemistry:
• Physics
• Computer science:
• Mathematics:
• The first and smallest transfinite ordinal number,[9] often identified with the set of natural numbers including 0 (sometimes written ${\displaystyle \omega _{0}}$)
• In set theory, ω1 is the first uncountable ordinal number[10] (also sometimes written as Ω)
• 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
• Clique number in Graph theory
• 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[11]
• In shift_JIS art, used to represent the cat's mouth. (e.g. (´･ω･`) ｼｮﾎﾞｰﾝ)
• In actuarial sciences, used to represent the maximum life span that characterizes a mortality table

## Character encodings

### Greek omega/Coptic oou

Character information
PreviewΩω
Unicode nameGREEK CAPITAL LETTER OMEGAGREEK SMALL LETTER OMEGACOPTIC CAPITAL LETTER OOUCOPTIC SMALL LETTER OOU
Encodingsdecimalhexdecimalhexdecimalhexdecimalhex
Unicode937U+03A9969U+03C911440U+2CB011441U+2CB1
UTF-8206 169CE A9207 137CF 89226 178 176E2 B2 B0226 178 177E2 B2 B1
Numeric character reference&#937;&#x3A9;&#969;&#x3C9;&#11440;&#x2CB0;&#11441;&#x2CB1;
Named character reference&ohm;, &Omega;&omega;
DOS Greek15197224E0
DOS Greek-2213D5250FA
Windows 1253217D9249F9
TeX\Omega\omega

[12]

### Cyrillic omega

Character information
PreviewѠѡ
Unicode nameCYRILLIC CAPITAL LETTER OMEGACYRILLIC SMALL LETTER OMEGACOMBINING CYRILLIC LETTER OMEGA
Encodingsdecimalhexdecimalhexdecimalhex
Unicode1120U+04601121U+046142619U+A67B
UTF-8209 160D1 A0209 161D1 A1234 153 187EA 99 BB
Numeric character reference&#1120;&#x460;&#1121;&#x461;&#42619;&#xA67B;
Character information
PreviewѺѻ
Unicode nameCYRILLIC CAPITAL LETTER ROUND OMEGACYRILLIC SMALL LETTER ROUND OMEGACYRILLIC CAPITAL LETTER BROAD OMEGACYRILLIC SMALL LETTER BROAD OMEGA
Encodingsdecimalhexdecimalhexdecimalhexdecimalhex
Unicode1146U+047A1147U+047B42572U+A64C42573U+A64D
UTF-8209 186D1 BA209 187D1 BB234 153 140EA 99 8C234 153 141EA 99 8D
Numeric character reference&#1146;&#x47A;&#1147;&#x47B;&#42572;&#xA64C;&#42573;&#xA64D;

### Latin/IPA omega

Character information
Previewɷ
Unicode nameLATIN SMALL LETTER CLOSED OMEGALATIN CAPITAL LETTER OMEGALATIN SMALL LETTER OMEGA
Encodingsdecimalhexdecimalhexdecimalhex
Unicode631U+027742934U+A7B642935U+A7B7
UTF-8201 183C9 B7234 158 182EA 9E B6234 158 183EA 9E B7
Numeric character reference&#631;&#x277;&#42934;&#xA7B6;&#42935;&#xA7B7;

### Technical omega symbols

Character information
Preview
Unicode nameAPL FUNCTIONAL SYMBOL OMEGAAPL FUNCTIONAL SYMBOL OMEGA UNDERBAROHM SIGNINVERTED OHM SIGN
Encodingsdecimalhexdecimalhexdecimalhexdecimalhex
Unicode9077U+23759081U+23798486U+21268487U+2127
UTF-8226 141 181E2 8D B5226 141 185E2 8D B9226 132 166E2 84 A6226 132 167E2 84 A7
Numeric character reference&#9077;&#x2375;&#9081;&#x2379;&#8486;&#x2126;&#8487;&#x2127;
Named character reference&mho;

### Mathematical omega

Character information
Preview𝛀𝛚𝛺𝜔𝜴𝝎
Unicode nameMATHEMATICAL 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
Encodingsdecimalhexdecimalhexdecimalhexdecimalhexdecimalhexdecimalhex
Unicode120512U+1D6C0120538U+1D6DA120570U+1D6FA120596U+1D714120628U+1D734120654U+1D74E
UTF-8240 157 155 128F0 9D 9B 80240 157 155 154F0 9D 9B 9A240 157 155 186F0 9D 9B BA240 157 156 148F0 9D 9C 94240 157 156 180F0 9D 9C B4240 157 157 142F0 9D 9D 8E
UTF-1655349 57024D835 DEC055349 57050D835 DEDA55349 57082D835 DEFA55349 57108D835 DF1455349 57140D835 DF3455349 57166D835 DF4E
Numeric character reference&#120512;&#x1D6C0;&#120538;&#x1D6DA;&#120570;&#x1D6FA;&#120596;&#x1D714;&#120628;&#x1D734;&#120654;&#x1D74E;
Character information
Preview𝝮𝞈𝞨𝟂
Unicode nameMATHEMATICAL SANS-SERIF
BOLD CAPITAL OMEGA
MATHEMATICAL SANS-SERIF
BOLD SMALL OMEGA
MATHEMATICAL SANS-SERIF
BOLD ITALIC CAPITAL OMEGA
MATHEMATICAL SANS-SERIF
BOLD ITALIC SMALL OMEGA
Encodingsdecimalhexdecimalhexdecimalhexdecimalhex
Unicode120686U+1D76E120712U+1D788120744U+1D7A8120770U+1D7C2
UTF-8240 157 157 174F0 9D 9D AE240 157 158 136F0 9D 9E 88240 157 158 168F0 9D 9E A8240 157 159 130F0 9D 9F 82
UTF-1655349 57198D835 DF6E55349 57224D835 DF8855349 57256D835 DFA855349 57282D835 DFC2
Numeric character reference&#120686;&#x1D76E;&#120712;&#x1D788;&#120744;&#x1D7A8;&#120770;&#x1D7C2;

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 the style of the text.

## Notes

1. "omega". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
2. The Greek Alphabet
3. Anne Jeffery (1961), The local scripts of archaic Greece, p.37–38.
4. Herbert Weir Smyth. A Greek Grammar for Colleges. §1
5. Edward M. Thompson (1912), Introduction to Greek and Latin paleography, Oxford: Clarendon. p.144
6. Capilla, José E.; Arevalo, Javier Rodriguez; Castaño, Silvino Castaño; Teijeiro, María Fé Díaz; del Moral, Rut Sanchez; Diaz, Javier Heredia (19 September 2012). "Mapping Oxygen-18 in Meteoric Precipitation over Peninsular Spain using Geostatistical Tools" (PDF). cedex.es. Valencia, Spain: Ninth Conference on Geostatistics for Environmental Applications. Retrieved 8 May 2017.
7. Excerpts from The Unicode Standard, Version 4.0. Retrieved 11 October 2006.
8. Weisstein, Eric W. "Prime Factor". mathworld.wolfram.com. Retrieved 12 August 2020.
9. "Compendium of Mathematical Symbols". Math Vault. 1 March 2020. Retrieved 12 August 2020.
10. "first uncountable ordinal in nLab". ncatlab.org. Retrieved 12 August 2020.
11. "Definition of Omega Male, BuzzWord from Macmillan Dictionary". macmillandictionary.com. Retrieved 10 February 2021.
12. Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)