omega

{{about|the Greek letter|the Cyrillic letter|Omega (Cyrillic)|the Latin letter |Latin omega}}

{{Greek Alphabet|letter=omega}}Omega ({{IPAc-en|US|oʊ|ˈ|m|eɪ|ɡ|ə|,_|-|ˈ|m|ɛ|ɡ|ə|,_|-|ˈ|m|iː|ɡ|ə|audio=LL-Q1860 (eng)-Flame, not lame-Omega.wav}}, {{IPAc-en|UK|ˈ|oʊ|m|ɪ|ɡ|ə|}};{{cite LPD|3|omega}} uppercase Ω, lowercase ω; Ancient Greek ὦ, later ὦ μέγα, Modern Greek ωμέγα) is the twenty-fourth and last letter in the Greek alphabet. In the Greek numeric system/isopsephy (gematria), it has a value of 800. The word literally means "great O" (o mega, mega meaning "great"), as opposed to omicron, which means "little O" (o mikron, mikron meaning "little").{{cite web |url=http://www.quinapalus.com/gr0.1.html |title=The Greek Alphabet }}

In phonetic terms, the Ancient Greek Ω represented a long open-mid back rounded vowel {{IPA|el|ɔː|IPA}}, comparable to the "aw" of the English word raw in dialects without the cot–caught merger, in contrast to omicron, which represented the close-mid back rounded vowel {{IPA|el|o|IPA}}, and the digraph ου, which represented the long close-mid back rounded vowel {{IPA|el|oː|IPA}}. In Modern Greek, both omega and omicron represent the mid back rounded vowel {{IPA|el|o̞|IPA}} or {{IPA|el|ɔ̝|IPA}}. The letter omega is transliterated into a Latin-script alphabet as 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 {{IPA|[ɔː]}}. It is a variant of omicron (Ο), broken up at the side (x16px), with the edges subsequently turned outward ({{GrGl|Omega 09}}, {{GrGl|Omega 05}}, {{GrGl|Omega 03}}, {{GrGl|Omega 07}}).Anne Jeffery (1961), The Local Scripts of Archaic Greece, pp. 37–38. 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 {{IPA|/o/}}.

The name Ωμέγα is Byzantine; in Classical Greek, the letter was called ō ({{lang|grc|ὦ}}) (pronounced /ɔ̂ː/), whereas the omicron was called ou ({{lang|grc|οὖ}}) (pronounced /ôː/).Herbert Weir Smyth A Greek Grammar for Colleges §1. The modern lowercase shape goes back to the uncial form x14px, a form that developed during the 3rd century BC in ancient handwriting on papyrus, from a flattened-out form of the letter (x16px) that had its edges curved even further upward.Edward M. Thompson (1912), Introduction to Greek and Latin Paleography, Oxford: Clarendon, p. 144.

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's in sparse use (see Latin omega).

The symbol Ω (uppercase letter)

File:Kos città, piazza eleftherias, edificio razionalista, targa.JPG 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{{cite web |last1=Capilla |first1=José E. |last2=Arevalo |first2=Javier Rodriguez |last3=Castaño |first3=Silvino Castaño |last4=Teijeiro |first4=María Fé Díaz |last5=del Moral |first5=Rut Sanchez |last6=Diaz |first6=Javier Heredia |title=Mapping Oxygen-18 in Meteoric Precipitation over Peninsular Spain Using Geostatistical Tools |url=http://www.cedex.es/NR/rdonlyres/B8A9522A-5D6F-4675-921A-24BB8458187B/124720/Capilla_et_al_geoENV_2012_Valencia_Espa%C3%B1a_Extended.pdf |website=cedex.es |publisher=Ninth Conference on Geostatistics for Environmental Applications |location=Valencia, Spain |date=19 September 2012 |access-date=8 May 2017 |archive-date=23 September 2015 |archive-url=https://web.archive.org/web/20150923201512/http://www.cedex.es/NR/rdonlyres/B8A9522A-5D6F-4675-921A-24BB8458187B/124720/Capilla_et_al_geoENV_2012_Valencia_Espa%C3%B1a_Extended.pdf |url-status=dead }}
For omega 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.{{Cite journal |last=Krishna |first=Mallela M. G. |last2=Lin |first2=Yan |last3=Rumbley |first3=Jon N. |last4=Walter Englander |first4=S. |date=2003-08-01 |title=Cooperative Omega Loops in Cytochrome c: Role in Folding and Function |url=https://www.sciencedirect.com/science/article/abs/pii/S0022283603006971 |journal=Journal of Molecular Biology |volume=331 |issue=1 |pages=29–36 |doi=10.1016/S0022-2836(03)00697-1 |issn=0022-2836|url-access=subscription }}
In physics:
For ohm – SI unit of electrical resistance.{{Cite web |date=2025-01-03 |title=Ohm {{!}} Electricity, Resistance & Voltage {{!}} Britannica |url=https://www.britannica.com/science/ohm |access-date=2025-02-08 |website=www.britannica.com |language=en}} Unicode has a separate code point {{unichar|2126|OHM SIGN}} (HTML entity &ohm;), but it is included only for backward compatibility, and the canonically equivalent code point {{unichar|03A9|GREEK CAPITAL LETTER OMEGA}} (Ω) is preferred. Also formerly also used upside down ({{unichar|2127|INVERTED OHM SIGN}}) to represent mho, the old name for the inverse of an ohm (now siemens with symbol S), the SI unit of electrical conductance.Excerpts from [https://www.unicode.org/versions/Unicode4.0.0/ch07.pdf#search=%22character%20U%2B2126%20maps%20OR%20map%20OR%20mapping%22 The Unicode Standard, Version 4.0]. Retrieved 11 October 2006.
In statistical mechanics, Ω refers to the multiplicity (number of microstates) in a system.
The solid angle{{Cite web |last=Weisstein |first=Eric W. |title=Solid Angle |url=https://mathworld.wolfram.com/SolidAngle.html |access-date=2025-02-07 |website=mathworld.wolfram.com |language=en |quote=The solid angle Ω subtended by a surface S is defined as the surface area Ω of a unit sphere covered by the surface's projection onto the sphere.}} or the rate of precession in a gyroscope
In particle physics to represent the Omega baryons
In astronomy (cosmology), Ω refers to the average 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{{Cite web |last=Weisstein |first=Eric W. |title=Omega Constant |url=https://mathworld.wolfram.com/OmegaConstant.html |access-date=2025-01-18 |website=mathworld.wolfram.com |language=en}}
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 triangle geometry, Brocard points{{Cite web |last=Weisstein |first=Eric W. |title=Brocard Points |url=https://mathworld.wolfram.com/BrocardPoints.html |access-date=2025-02-07 |website=mathworld.wolfram.com |language=en}}
In number theory, Ω(n) is the number of prime divisors of n (counting multiplicity).{{Cite web |last=Weisstein |first=Eric W. |title=Prime Factor |url=https://mathworld.wolfram.com/PrimeFactor.html |website=mathworld.wolfram.com |access-date=12 August 2020 }}
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, ω₁ or Ω
The absolute infinite proposed by Georg Cantor.
As part of a logo or trademark:
The logo of Omega Watches SA{{Cite web|url=https://www.hallandladdco.com/blogs/interesting-articles/the-history-of-the-omega-watch-company|title=The History Of The Omega Watch Company|website=HallandLaddco|language=en|access-date=2019-02-02|archive-date=March 19, 2020|archive-url=https://web.archive.org/web/20200319035901/https://www.hallandladdco.com/blogs/interesting-articles/the-history-of-the-omega-watch-company|url-status=dead}}
Part of the original Pioneer logo{{Cite web |title=Pioneer Logo, symbol, meaning, history, PNG, brand |url=https://logos-world.net/pioneer-logo/ |access-date=2025-02-08 |language=en-US |quote=The logo features a tuning fork surrounded by the Greek letter Omega.}}
Part of the Badge of the Supreme Court of the United Kingdom{{Cite web |date=2022-05-07 |title=Emblem of the Supreme Court - Herald Art |url=https://heraldart.co.uk/emblem-of-the-supreme-court/ |access-date=2025-02-08 |language=en-GB |quote=The emblem shows the plant badges of England and Wales, Scotland and Northern Ireland surrounded by Omega the ultimate letter in the Greek alphabet.}}
Part of the mission patch for STS-135, as it was the last mission of the Space Shuttle program{{Cite web |title=STS-135 / Atlantis mission patch - collectSPACE: Messages |url=http://www.collectspace.com/ubb/Forum18/HTML/000805.html |access-date=2025-02-08 |website=www.collectspace.com |quote=Omega, the last letter in the Greek alphabet, recognizes this mission as the last flight 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
The logo of Lalaji Memorial Omega International School

File:Fachada de Panteón de la Cruz.jpg, representing the end of life{{cite web |title=Desde la Revolución hasta el 2020 |url=https://www.aguascalientes.gob.mx/territoriojoven/revolucion2020 |website=Gobierno de Aguascalientes |access-date=7 August 2024 |quote=...su fachada representa a una omega que simboliza el final de la vida.}}]]

Other:
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{{Cite web |date=2013-10-16 |title=6 Ridiculous Sci-Fi Energy Schemes |url=https://www.popularmechanics.com/culture/g1338/6-ridiculous-sci-fi-energy-schemes/ |access-date=2025-02-07 |website=Popular Mechanics |language=en-US |quote=But the writers of one episode of Star Trek: Voyager apparently slept through that lecture, as they introduced the omega particle in "The Omega Directive."}}
The final form of NetNavi bosses in some of the Mega Man Battle Network games
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
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.{{cite web | url=http://www.substancenews.net/articles.php?page=6592 | title=Resistance should begin now - Substance News }}
It's used along with Alpha in the Alpha and Omega, a Christian symbol.{{CathEncy|wstitle= A and Ω |volume= 1 |page= 332 |last= Hassett |first= M.M. |author-link= |year=1913|short= 1}}
Used as the highest tier of equipment in the flash game, Learn to Fly
Appears in galaxy quest as the Omega 13 device

The symbol ω (lowercase letter)

The minuscule letter ω is used as a symbol:

Biology, biochemistry and chemistry:
In biochemistry, for one of the RNA polymerase subunits
In biology, for fitness
In chemistry, for denoting the carbon atom furthest from the carboxyl group of a fatty acid
In genomics, as a measure of molecular evolution in protein-coding genes (also denoted as d_N/d_S or K_a/K_s ratio)
Physics:
Angular velocity or angular frequency{{Citation |last=Elert |first=Glenn |title=Special Symbols |date=2023 |work=The Physics Hypertextbook |quote= ω angular frequency|url=https://physics.info/symbols/ |access-date=2025-02-01 |publisher=hypertextbook |language=en}}
Rotation velocity (bold), rotational speed or frequency{{Citation |last=Elert |first=Glenn |title=Special Symbols |date=2023 |work=The Physics Hypertextbook |quote= ω, ω rotational velocity, rotational speed|url=https://physics.info/symbols/ |access-date=2025-02-01 |publisher=hypertextbook |language=en}}
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 angular 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{{cite journal |last=Maglich |first=B. |date=1976 |title=Discovery of omega meson-first neutral vector meson: one researcher's account - Discovery story |url=https://inspirehep.net/files/bed57fc443ad4a089648fd0574f4d256 |journal=Advanced Experimental Physics |volume=5 |pages=79–105 |quote=Omega Meson Observed (page 97)}}
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
In APL, to represent the right parameter to a function
Mathematics:
The first and smallest transfinite ordinal number, often identified with the set of natural numbers including 0 (sometimes written $\omega_0$ ){{Cite web |last=Weisstein |first=Eric W. |title=Ordinal Number |url=https://mathworld.wolfram.com/OrdinalNumber.html |access-date=2025-01-18 |website=mathworld.wolfram.com |language=en |quote=The first transfinite ordinal, denoted ω, is ...}}{{Citation |last=Easwaran |first=Kenny |title=Infinity |date=2024 |work=The Stanford Encyclopedia of Philosophy |editor-last=Zalta |editor-first=Edward N. |url=https://plato.stanford.edu/entries/infinity/ |access-date=2025-02-07 |edition=Summer 2024 |publisher=Metaphysics Research Lab, Stanford University |last2=Hájek |first2=Alan |last3=Mancosu |first3=Paolo |last4=Oppy |first4=Graham |editor2-last=Nodelman |editor2-first=Uri}}
In set theory, ω is the ordinal number{{Cite web |title=first uncountable ordinal in nLab |url=https://ncatlab.org/nlab/show/first+uncountable+ordinal |website=NCatLab.org |access-date=12 August 2020 }}
A primitive root of unity, like the complex cube roots of 1
The Wright Omega function{{Cite web |last=Weisstein |first=Eric W. |title=Wright Function |url=https://mathworld.wolfram.com/WrightFunction.html |access-date=2025-01-18 |website=mathworld.wolfram.com |language=en}}
A generic differential form
In number theory, ω(n) is the number of distinct prime divisors of n{{Cite web |last=Weisstein |first=Eric W. |title=Distinct Prime Factors |url=https://mathworld.wolfram.com/DistinctPrimeFactors.html |access-date=2025-02-08 |website=mathworld.wolfram.com |language=en |quote=The distinct prime factors of a positive integer n>=2 are defined as the ω(n) numbers p_1, ..., p_(ω(n))...}}
In number theory, an arithmetic function
In combinatory logic, the self-application combinator, (λ x. x x)
In triangle geometry, a Brocard angle{{Cite web |last=Weisstein |first=Eric W. |title=Brocard Angle |url=https://mathworld.wolfram.com/BrocardAngle.html |access-date=2025-02-07 |website=mathworld.wolfram.com |language=en}}
Clique number in Graph theory{{Cite web |last=Weisstein |first=Eric W. |title=Clique |url=https://mathworld.wolfram.com/Clique.html |access-date=2025-02-07 |website=mathworld.wolfram.com |language=en |quote=A clique of a graph G is a complete subgraph of G, and the clique of largest possible size is referred to as a maximum clique (which has size known as the (upper) clique number ?(G)).}}
Finance:
In finance, the elasticity of 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{{Cite web |title=Definition of Omega Male, BuzzWord from Macmillan Dictionary |url=https://www.macmillandictionary.com/buzzword/entries/omega-male.html |website=macmillandictionary.com |access-date=10 February 2021 }}
In economics (specifically like in general equilibrium theory), the endowments of agents
In shift_JIS art, used to represent the cat's mouth. (e.g. {{lang|ja|(´･ω･`) ｼｮﾎﾞｰﾝ}})
In actuarial sciences, used to represent the maximum life span that characterizes a mortality table{{Cite web |title=Life Table — Solving Actuarial Math with Python |url=https://actuarialmath-guide.readthedocs.io/en/latest/lifetable.html |access-date=2025-02-08 |website=actuarialmath-guide.readthedocs.io |quote=A life table, from some initial age x0 to a maximum age ω, represents a survival model with probabilities...}}

Unicode

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References

External links

{{Commons category-inline}}
{{Wiktionary-inline|Ω|ω}}

Category:Greek letters

Category:Vowel letters