Omega

Omega(US:/oʊˈmeɪɡə,-ˈmɛɡə,-ˈmiːɡə/,UK:/ˈoʊmɪɡə/;^[1]uppercaseΩ,lowercaseω;Ancient Greekὦ, later ὦ μέγα,Modern Greekωμέγα) is the twenty-fourth and last letter in theGreek alphabet.In theGreek numeric system/isopsephy(gematria), it has a value of 800. The word literally means "great O" (o mega,mega meaning "great" ), as opposed toomicron,which means "little O" (o mikron,micron meaning "little" ).^[2]

Inphoneticterms, the Ancient Greek Ω represented along open-mid back rounded vowelIPA:[ɔː],comparable to the "aw" of theEnglishwordrawin dialects without thecot–caught merger,in contrast toomicronwhich represented theclose-mid back rounded vowelIPA:[o],and thedigraphουwhich represented thelong close-mid back rounded vowelIPA:[oː].InModern Greek,both omega and omicron represent themid back rounded vowelIPA:[o̞]orIPA:[ɔ̝].The letter omega istransliteratedinto aLatin-script alphabetasōor simplyo.

As the final letter in the Greek alphabet, omega is often used to denote the last, the end, or the ultimate limit of aset,in contrast toalpha,the first letter of the Greek alphabet; seeAlpha 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 along 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 ofKnidosas well as a few Aegean islands, namelyParos,ThasosandMelos,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 isByzantine;inClassical Greek,the letter was calledō(ὦ) (pronounced /ɔ̂ː/), whereas the omicron was calledou(οὖ) (pronounced /ôː/).^[4] The modern lowercase shape goes back to theuncialform,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 theearly Cyrillic alphabet(seeCyrillic omega(Ѡ, ѡ)). ARaeticvariant is conjectured to be at the origin or parallel evolution of theElder Futhark ᛟ.

Omega was also adopted into the Latin alphabet, as a letter of the 1982 revision to theAfrican reference alphabet.It's in sparse use (seeLatin omega).

The symbol Ω (uppercase letter)

Plaque inKoswith "underlined O" form of omega

Theuppercaseletter Ω is used as a symbol:

Inchemistry:
- Foroxygen-18,a natural, stable isotope of oxygen^[6]
- Foromega loop,a protein structural motif consisting of a loop of six or more amino acid residues in any sequence, a structure named for its resemblance to the Greek letter.
Inphysics:
- Forohm– SI unit of electrical resistance; formerly also used upside down (℧) to representmho,the old name for the inverse of an ohm (now siemens with symbol S) used for electrical conductance. Unicode has a separate code pointU+2126ΩOHM SIGN(HTML entity&ohm;), but it is included only for backward compatibility, and the canonically equivalent code pointU+03A9ΩGREEK CAPITAL LETTER OMEGA(Ω) is preferred.^[7]
- Instatistical mechanics,Ω refers to the multiplicity (number of microstates) in a system.
- Thesolid angleor the rate of precession in a gyroscope
- In particle physics to represent theOmega baryons
- In astronomy (cosmology), Ω refers to the average density of the universe, also called thedensity parameter.
- In astronomy (orbital mechanics), Ω refers to thelongitude of the ascending nodeof an orbit.
Inmathematicsandcomputer science:
- In complex analysis, theOmega constant,a solution of Lambert's W function
- In differential geometry, the space ofdifferential formson amanifold(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 classifierof an elementary topos.
- Incombinatory logic,the looping combinator,(S I I (S I I))
- In group theory, theomega and agemo subgroupsof ap-group, Ω(G) and ℧(G)
- In group theory,Cayley's Ω processas a partial differential operator.
- In statistics, it is used as the symbol for thesample space,or total set of possible outcomes.
- Intriangle geometry,Brocard points
- Innumber theory,Ω(n)is the number ofprime divisorsofn(countingmultiplicity).^[8]
- In notation related toBig O notationto describe the asymptotic behavior of functions.
- Chaitin's constant.
- Inset theory,thefirst uncountable ordinal number,ω₁or Ω
- Theabsolute infiniteproposed byGeorg Cantor.
As part of logo or trademark:
- The logo ofOmega WatchesSA
- Part of the originalPioneerlogo
- Part of theBadge of the Supreme Courtof the United Kingdom
- Part of the mission patch forSTS-135,as it was the last mission of the Space Shuttle program
- The logo of theGod of Warvideo 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 ofE-123 Omega,aSonic the Hedgehogcharacter.
- The logo of theHeroes of Olympusseries, based on Greek mythology.
- the logo of theUltramarinesinWarhammer 40,000
- The logo of Primal Groudon, the version mascot ofPokémon Omega Ruby.
- The logo ofDarkseidin DC comics
- One of the logos of professional wrestlerKenny Omega
- The logo forMeow Wolf'sOmega Martin Area15, Las Vegas, Nevada
- The logo ofLalaji Memorial Omega International School

Omega-shaped entrance to the Panteón de la Cruz inAguascalientes,representing the end of life.^[9]

Other:
- Ineschatology,the symbol for the end of everything
- Inmolecular biology,the symbol is used as shorthand to signify a genetic construct introduced by atwo-point crossover
- Omega Particle in theStar Trek universe
- The final form of NetNavi bosses in some of theMega Man Battle Networkgames
- A secret boss in theFinal Fantasyseries called Omega ( Ω ) Weapon.
- A character from the seriesDoctor Whocalled Omega, believed to be one of the creators of the Time Lords of Gallifrey.
- The symbol for the highest power level of aPSIattack in theMother/EarthBoundgames
- A symbol used by U.S. citizens in the 1960s & 1970s to denote resistance to the U.S. war in Viet Nam. Adapted from the SI unit for electrical resistance.^[10]
- It's used along withAlphain theAlpha and Omega,a Christian symbol.

The symbol ω (lowercase letter)

Theminusculeletter ω is used as a symbol:

Biology, biochemistry and chemistry:
- Inbiochemistry,for one of theRNA polymerasesubunits
- In biology, forfitness
- Inchemistry,for denoting the carbon atom furthest from thecarboxyl groupof afatty acid
- Ingenomics,as a measure ofmolecular evolutionin protein-coding genes (also denoted as d_N/d_SorK_a/K_sratio)
Physics:
- Angular velocityorangular frequency
- Incomputational fluid dynamics,the specific turbulence dissipation rate
- Inmeteorology,the change of pressure with respect to time of aparcelof air
- Incircuit analysisandsignal processingto representangular frequency,related tofrequencyfby ω = 2πf
- Inastronomy,as a ranking of a star's brightness within a constellation
- Inorbital mechanics,as designation of theargument of periapsisof an orbit
- Inparticle physicsto represent theomega meson
Computer science:
- In notation related toBig O notation,theasymptotically dominantnature offunctions
- Inrelational databasetheory to representNULL,a missing or inapplicable value
- InAPL,to represent the right parameter to a function
Mathematics:
- The first and smallesttransfinite ordinal number,often identified with the set of natural numbers including 0 (sometimes written $\omega _{0}$ )
- Inset theory,ω is theordinal number^[11]
- A primitiveroot of unity,like the complex cube roots of 1
- TheWright Omega function
- A genericdifferential form
- Innumber theory,ω(n) is the number of distinctprime divisorsofn
- Innumber theory,anarithmetic function
- Incombinatory logic,the self-application combinator,(λ x. x x)
- Intriangle geometry,aBrocard angle
- Clique numberinGraph theory
Finance:
- In finance, the elasticity ofoptions
- In analytical investment management, thetracking errorof an investment manager
Other:
- Used in place ofんin Japanese typing shorthand.
- Inlinguistics,thephonological word
- Intextual criticism,thearchetypeof a manuscript tradition
- Insociology,used to refer to the lowest ranking member of a group^[12]
- Ineconomics(specifically like in general equilibrium theory), the endowments of agents
- Inshift_JIS art,used to represent the cat's mouth. (e.g.(´･ω･`) ｼｮﾎﾞｰﾝ)
- Inactuarial sciences,used to represent the maximum life span that characterizes amortality table

Unicode

U+0277ɷLATIN SMALL LETTER CLOSED OMEGA^[13]
U+038FΏGREEK CAPITAL LETTER OMEGA WITH TONOS
U+03A9ΩGREEK CAPITAL LETTER OMEGA(&ohm;, Ω)
U+03C9ωGREEK SMALL LETTER OMEGA(ω)
U+03CEώGREEK SMALL LETTER OMEGA WITH TONOS
U+03D6ϖGREEK PI SYMBOL(ϖ, ϖ)
U+0460ѠCYRILLIC CAPITAL LETTER OMEGA
U+0461ѡCYRILLIC SMALL LETTER OMEGA
U+047AѺCYRILLIC CAPITAL LETTER ROUND OMEGA
U+047BѻCYRILLIC SMALL LETTER ROUND OMEGA
U+047CѼCYRILLIC CAPITAL LETTER OMEGA WITH TITLO
U+047DѽCYRILLIC SMALL LETTER OMEGA WITH TITLO
U+1F60ὠGREEK SMALL LETTER OMEGA WITH PSILI
U+1F61ὡGREEK SMALL LETTER OMEGA WITH DASIA
U+1F62ὢGREEK SMALL LETTER OMEGA WITH PSILI AND VARIA
U+1F63ὣGREEK SMALL LETTER OMEGA WITH DASIA AND VARIA
U+1F64ὤGREEK SMALL LETTER OMEGA WITH PSILI AND OXIA
U+1F65ὥGREEK SMALL LETTER OMEGA WITH DASIA AND OXIA
U+1F66ὦGREEK SMALL LETTER OMEGA WITH PSILI AND PERISPOMENI
U+1F67ὧGREEK SMALL LETTER OMEGA WITH DASIA AND PERISPOMENI
U+1F68ὨGREEK CAPITAL LETTER OMEGA WITH PSILI
U+1F69ὩGREEK CAPITAL LETTER OMEGA WITH DASIA
U+1F6AὪGREEK CAPITAL LETTER OMEGA WITH PSILI AND VARIA
U+1F6BὫGREEK CAPITAL LETTER OMEGA WITH DASIA AND VARIA
U+1F6CὬGREEK CAPITAL LETTER OMEGA WITH PSILI AND OXIA
U+1F6DὭGREEK CAPITAL LETTER OMEGA WITH DASIA AND OXIA
U+1F6EὮGREEK CAPITAL LETTER OMEGA WITH PSILI AND PERISPOMENI
U+1F6FὯGREEK CAPITAL LETTER OMEGA WITH DASIA AND PERISPOMENI
U+1F7CὼGREEK SMALL LETTER OMEGA WITH VARIA
U+1F7DώGREEK SMALL LETTER OMEGA WITH OXIA
U+1FA0ᾠGREEK SMALL LETTER OMEGA WITH PSILI AND YPOGEGRAMMENI
U+1FA1ᾡGREEK SMALL LETTER OMEGA WITH DASIA AND YPOGEGRAMMENI
U+1FA2ᾢGREEK SMALL LETTER OMEGA WITH PSILI AND VARIA AND YPOGEGRAMMENI
U+1FA3ᾣGREEK SMALL LETTER OMEGA WITH DASIA AND VARIA AND YPOGEGRAMMENI
U+1FA4ᾤGREEK SMALL LETTER OMEGA WITH PSILI AND OXIA AND YPOGEGRAMMENI
U+1FA5ᾥGREEK SMALL LETTER OMEGA WITH DASIA AND OXIA AND YPOGEGRAMMENI
U+1FA6ᾦGREEK SMALL LETTER OMEGA WITH PSILI AND PERISPOMENI AND YPOGEGRAMMENI
U+1FA7ᾧGREEK SMALL LETTER OMEGA WITH DASIA AND PERISPOMENI AND YPOGEGRAMMENI
U+1FA8ᾨGREEK CAPITAL LETTER OMEGA WITH PSILI AND PROSGEGRAMMENI
U+1FA9ᾩGREEK CAPITAL LETTER OMEGA WITH DASIA AND PROSGEGRAMMENI
U+1FAAᾪGREEK CAPITAL LETTER OMEGA WITH PSILI AND VARIA AND PROSGEGRAMMENI
U+1FABᾫGREEK CAPITAL LETTER OMEGA WITH DASIA AND VARIA AND PROSGEGRAMMENI
U+1FACᾬGREEK CAPITAL LETTER OMEGA WITH PSILI AND OXIA AND PROSGEGRAMMENI
U+1FADᾭGREEK CAPITAL LETTER OMEGA WITH DASIA AND OXIA AND PROSGEGRAMMENI
U+1FAEᾮGREEK CAPITAL LETTER OMEGA WITH PSILI AND PERISPOMENI AND PROSGEGRAMMENI
U+1FAFᾯGREEK CAPITAL LETTER OMEGA WITH DASIA AND PERISPOMENI AND PROSGEGRAMMENI
U+1FF2ῲGREEK SMALL LETTER OMEGA WITH VARIA AND YPOGEGRAMMENI
U+1FF3ῳGREEK SMALL LETTER OMEGA WITH YPOGEGRAMMENI
U+1FF4ῴGREEK SMALL LETTER OMEGA WITH OXIA AND YPOGEGRAMMENI
U+1FF6ῶGREEK SMALL LETTER OMEGA WITH PERISPOMENI
U+1FF7ῷGREEK SMALL LETTER OMEGA WITH PERISPOMENI AND YPOGEGRAMMENI
U+1FFAῺGREEK CAPITAL LETTER OMEGA WITH VARIA
U+1FFBΏGREEK CAPITAL LETTER OMEGA WITH OXIA
U+1FFCῼGREEK CAPITAL LETTER OMEGA WITH PROSGEGRAMMENI
U+2375⍵APL FUNCTIONAL SYMBOL OMEGA
U+2379⍹APL FUNCTIONAL SYMBOL OMEGA UNDERBAR
U+2CB0ⲰCOPTIC CAPITAL LETTER OOU
U+2CB1ⲱCOPTIC SMALL LETTER OOU
U+2CBEⲾCOPTIC CAPITAL LETTER OLD COPTIC OOU
U+2CBFⲿCOPTIC SMALL LETTER OLD COPTIC OOU
U+A64CꙌCYRILLIC CAPITAL LETTER BROAD OMEGA
U+A64DꙍCYRILLIC SMALL LETTER BROAD OMEGA
U+A67BꙻCOMBINING CYRILLIC LETTER OMEGA
U+A7B6ꞶLATIN CAPITAL LETTER OMEGA
U+A7B7ꞷLATIN SMALL LETTER OMEGA
U+AB65ꭥGREEK LETTER SMALL CAPITAL OMEGA
U+107A4𐞤MODIFIER LETTER SMALL CLOSED OMEGA
U+1D6C0𝛀MATHEMATICAL BOLD CAPITAL OMEGA^[a]
U+1D6DA𝛚MATHEMATICAL BOLD SMALL OMEGA
U+1D6FA𝛺MATHEMATICAL ITALIC CAPITAL OMEGA
U+1D714𝜔MATHEMATICAL ITALIC SMALL OMEGA
U+1D734𝜴MATHEMATICAL BOLD ITALIC CAPITAL OMEGA
U+1D74E𝝎MATHEMATICAL BOLD ITALIC SMALL OMEGA
U+1D76E𝝮MATHEMATICAL SANS-SERIF BOLD CAPITAL OMEGA
U+1D788𝞈MATHEMATICAL SANS-SERIF BOLD SMALL OMEGA
U+1D7A8𝞨MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL OMEGA
U+1D7C2𝟂MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL OMEGA

^TheMATHEMATICALcharacters are used only in math. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate the style of the text.

References

^Wells, John C.(2008). "omega".Longman Pronunciation Dictionary(3rd ed.). Longman.ISBN 978-1-4058-8118-0.
^"The Greek Alphabet".
^^a ^bAnne 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
^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. Archived fromthe original(PDF)on 23 September 2015.Retrieved8 May2017.
^Excerpts fromThe Unicode Standard, Version 4.0.Retrieved 11 October 2006.
^Weisstein, Eric W."Prime Factor".mathworld.wolfram.com.Retrieved12 August2020.
^"Desde la Revolución hasta el 2020".Gobierno de Aguascalientes.Retrieved7 August2024....su fachada representa a una omega que simboliza el final de la vida.
^"Resistance should begin now - Substance News".
^"first uncountable ordinal in nLab".NCatLab.org.Retrieved12 August2020.
^"Definition of Omega Male, BuzzWord from Macmillan Dictionary".macmillandictionary.com.Retrieved10 February2021.
^Unicode Code Charts:Greek and Coptic (Range: 0370-03FF)

External links

Media related toOmega (letter)at Wikimedia Commons
The dictionary definition ofωat Wiktionary

[14] TheMATHEMATICALcharacters are used only in math. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate the style of the text.

[1] Wells, John C.(2008). "omega".Longman Pronunciation Dictionary(3rd ed.). Longman.ISBN 978-1-4058-8118-0.

[2] "The Greek Alphabet".

[Jeffery37f-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

[geoENV2012-6] 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. Archived fromthe original(PDF)on 23 September 2015.Retrieved8 May2017.

[7] Excerpts fromThe Unicode Standard, Version 4.0.Retrieved 11 October 2006.

[8] Weisstein, Eric W."Prime Factor".mathworld.wolfram.com.Retrieved12 August2020.

[9] "Desde la Revolución hasta el 2020".Gobierno de Aguascalientes.Retrieved7 August2024....su fachada representa a una omega que simboliza el final de la vida.

[10] "Resistance should begin now - Substance News".

[11] "first uncountable ordinal in nLab".NCatLab.org.Retrieved12 August2020.

[12] "Definition of Omega Male, BuzzWord from Macmillan Dictionary".macmillandictionary.com.Retrieved10 February2021.

[13] Unicode Code Charts:Greek and Coptic (Range: 0370-03FF)

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[a]