View source for Omega

{{Short description|Last letter of the Greek alphabet}}
{{Redirect|Ω|the unit of electrical resistance|Ohm}}
{{about|the Greek letter|the Cyrillic letter|Omega (Cyrillic)|the Latin letter |Latin omega}}
{{Other uses}}
{{More citations needed|date=December 2014}}
{{Use dmy dates|date=April 2023}}
{{Greek Alphabet|letter=omega}}

'''Omega''' ({{IPAc-en|US|oʊ|ˈ|m|eɪ|ɡ|ə|,_|-|ˈ|m|ɛ|ɡ|ə|,_|-|ˈ|m|iː|ɡ|ə}}, {{IPAc-en|UK|ˈ|oʊ|m|ɪ|ɡ|ə|}};<ref>{{cite LPD|3|omega}}</ref> <!-- <ref>{{OED|omega}}</ref><ref>{{cite Dictionary.com|omega}}</ref> -->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 numerals|Greek numeric system]]/[[isopsephy]] ([[gematria]]), it has a value of 800. The word literally means "great&nbsp;O" (''o mega'', mega meaning "great"), as opposed to [[omicron]], which means "little&nbsp;O" (''o mikron'', micron meaning "little").<ref>{{cite web |url=http://www.quinapalus.com/gr0.1.html |title=The Greek Alphabet }}</ref>

In [[Phonetics|phonetic]] terms, the Ancient Greek Ω represented a [[vowel length|long]] [[open-mid back rounded vowel]] {{IPA|el|ɔː|IPA}}, comparable to the "aw" of the [[English language|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 (orthography)|digraph]] ''ου'' which represented the [[vowel length|long]] [[close-mid back rounded vowel]] {{IPA|el|oː|IPA}}. In [[Modern Greek]], both omega and omicron represent the [[mid back rounded vowel]]<!-- not close-mid, see Arvanti (1999) - Illustrations of the IPA: Modern Greek. --> {{IPA|el|o̞|IPA}} or {{IPA|el|ɔ̝|IPA}}. The letter omega is [[transliteration|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 theory|set]], in contrast to [[Alpha (letter)|alpha]], the first letter of the Greek alphabet; see [[Alpha and Omega]].

==History==
Ω was not part of the early (8th century BC) [[Archaic Greek alphabets|Greek alphabets]]. It was introduced in the late 7th century BC in the Ionian cities of Asia Minor to denote a [[vowel length|long]] [[open-mid back rounded vowel]] {{IPA|[ɔː]}}. It is a variant of omicron (Ο), broken up at the side ([[File:Greek Omega 09.svg|x16px]]), with the edges subsequently turned outward ({{GrGl|Omega 09}}, {{GrGl|Omega 05}}, {{GrGl|Omega 03}}, {{GrGl|Omega 07}}).<ref name=Jeffery37f>Anne Jeffery (1961), ''The local scripts of archaic Greece'', p.37–38.</ref>
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/}}.<ref name=Jeffery37f/>

The name Ωμέγα is [[Medieval Greek|Byzantine]]; in [[Ancient Greek|Classical Greek]], the letter was called ''ō'' ({{lang|grc|ὦ}}) (pronounced /ɔ̂ː/), whereas the omicron was called ''ou'' ({{lang|grc|οὖ}}) (pronounced /ôː/).<ref>Herbert Weir Smyth. ''A Greek Grammar for Colleges''. §1</ref> 
The modern lowercase shape goes back to the [[uncial]] form [[File:Greek uncial Omega.svg|x14px]], a form that developed during the 3rd century BC in ancient handwriting on papyrus, from a flattened-out form of the letter ([[File:Greek Omega 08.svg|x16px]]) that had its edges curved even further upward.<ref>Edward M. Thompson (1912), ''Introduction to Greek and Latin paleography'', Oxford: Clarendon. p.144</ref>

In addition to the Greek alphabet, Omega was also adopted into the [[early Cyrillic alphabet]] (see [[omega (Cyrillic)|Cyrillic omega]] (Ѡ, ѡ)). A [[Raetic alphabet|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|thumb|Plaque in [[Kos]] with "underlined O" form of omega]]

The [[Upper case|uppercase]] letter Ω is used as a symbol:
* In [[chemistry]]:
** For [[oxygen-18]], a natural, stable isotope of oxygen<ref name="geoENV2012">{{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 }}</ref>
** 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.<ref>{{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}}</ref>
* In [[physics]]:
** For [[ohm]] – SI unit of electrical resistance;<ref>{{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}}</ref> 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 {{unichar|2126|OHM SIGN}} ([[HTML entity]] <code>&amp;ohm;</code>), but it is included only for backward compatibility, and the canonically equivalent code point {{unichar|03A9|GREEK CAPITAL LETTER OMEGA}} (<code>&amp;Omega;</code>) is preferred.<ref>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.</ref>
** In [[statistical mechanics]], Ω refers to the multiplicity (number of microstates) in a system.
** The [[solid angle]]<ref>{{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.}}</ref> or the rate of precession in a gyroscope
** In particle physics to represent the [[Omega baryon]]s
** 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<ref>{{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}}</ref>
** In differential geometry, the space of [[differential form]]s 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#Undecidability of combinatorial calculus|combinatory logic]], the looping combinator, ''(S I I (S I I))''
** In group theory, the [[omega and agemo subgroup]]s 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]]<ref>{{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}}</ref>
** In [[number theory]], [[Prime omega function|Ω(''n'')]] is the number of [[prime divisor]]s of ''n'' (counting [[Multiplicity (mathematics)|multiplicity]]).<ref>{{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 }}</ref>
** In notation related to [[Big O notation]] to describe the asymptotic behavior of functions.
** [[Chaitin's constant]].
** In [[set theory]], the [[first uncountable ordinal|first uncountable ordinal number]], ω<sub>1</sub> or Ω
** The [[absolute infinite]] proposed by [[Georg Cantor]].
* As part of logo or trademark:
** The logo of [[Omega Watches]] SA<ref>{{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}}</ref>
** Part of the original [[Pioneer Corporation|Pioneer]] logo<ref>{{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.}}</ref>
** Part of the [[Supreme Court of the United Kingdom|Badge of the Supreme Court]] of the United Kingdom<ref>{{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.}}</ref>
** Part of the mission patch for [[STS-135]], as it was the last mission of the Space Shuttle program<ref>{{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.}}</ref>
** The logo of the ''[[God of War (franchise)|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 [[Space Marines (Warhammer 40,000)|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|thumb|Omega-shaped entrance to the Panteón de la Cruz in [[Aguascalientes (city)|Aguascalientes]], representing the end of life<ref>{{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.}}</ref>]]
* 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 [[Crossover (genetic algorithm)#Two-point crossover|two-point crossover]]
** Omega Particle in the [[The Omega Directive|Star Trek universe]]<ref>{{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."}}</ref>
** 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 [[Psionics|PSI]] attack in the ''[[Mother (video game series)|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.<ref>{{cite web | url=http://www.substancenews.net/articles.php?page=6592 | title=Resistance should begin now - Substance News }}</ref>
** It's used along with [[Alpha]] in the [[Alpha and Omega]], a Christian symbol.<ref>{{CathEncy|wstitle= A and Ω |volume= 1 |page= 332 |last= Hassett |first= M.M. |author-link= |year=1913|short= 1}}</ref>
** Used as the [[Rank|highest tier]] of equipment in the [[Browser game|flash game]], Learn to Fly
** Appears in [[Galaxy Quest|galaxy quest]] as the [[Omega 13 device]]

== The symbol ω (lowercase letter) ==
The [[Lower case|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 (biology)|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<sub>N</sub>/d<sub>S</sub> or [[Ka/Ks ratio|K<sub>a</sub>/K<sub>s</sub> ratio]])
* Physics:
** [[Angular velocity]] or [[angular frequency]]<ref>{{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}}</ref>
** Rotation velocity (bold), [[Rotational frequency|rotational speed or frequency]]<ref>{{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}}</ref>
** In [[computational fluid dynamics]], the specific turbulence dissipation rate
** In [[meteorology]], the change of pressure with respect to time of a [[Fluid parcel|parcel]] of air
** In [[circuit analysis]] and [[signal processing]] to represent [[angular frequency]], related to [[frequency]] ''f'' by ω = 2π''f''
** 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 [[Meson|omega meson]]<ref>{{cite journal |last=Maglich |first=B. |date=1976 |title=Discovery of omega meson-first neutral vector meson: one researcher's personal account - Discovery story |url=https://inspirehep.net/files/bed57fc443ad4a089648fd0574f4d256 |journal=Advanced Experimental Physics |volume=5 |pages=79–105 |quote=Omega Meson Observed (page 97)}}</ref>
* Computer science:
** In notation related to [[Big O notation]], the [[Asymptotical dominance|asymptotically dominant]] nature of [[Function (mathematics)|functions]]
** In [[relational database]] theory to represent [[Null (SQL)|NULL]], a missing or inapplicable value
** In [[APL (programming language)|APL]], to represent the right parameter to a function
* Mathematics:
** The first and smallest [[Transfinite number|transfinite]] [[ordinal number]], often identified with the set of natural numbers including 0 (sometimes written <math>\omega_0</math>)<ref>{{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 ...}}</ref><ref>{{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}}</ref>
** In [[set theory]], ω is the [[ordinal number]]<ref>{{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 }}</ref>
** A primitive [[Roots of unity|root of unity]], like the complex cube roots of 1
** The [[Wright Omega function]]<ref>{{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}}</ref>
** A generic [[differential form]]
** In [[number theory]], ω(''n'') is the number of distinct [[prime divisor]]s of ''n''<ref>{{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))...}}</ref>
** In [[number theory]], an [[arithmetic function]]
** In [[combinatory logic]], the self-application combinator, ''(λ x. x x)''
** In [[triangle geometry]], a [[Brocard angle]]<ref>{{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}}</ref>
** [[Clique number]] in [[Graph theory]]<ref>{{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)).}}</ref>
* Finance:
** In finance, the elasticity of [[Option (finance)|options]]
** In analytical investment management, the [[tracking error]] of an investment manager
* Other:
** Used in place of [[N (kana)|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<ref>{{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 }}</ref>
** 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 science|actuarial sciences]], used to represent the maximum life span that characterizes a [[mortality table]]<ref>{{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...}}</ref>

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{{notelist}}

==References==
{{Reflist}}

==External links==
* {{Commons category-inline}}
* {{Wiktionary-inline|Ω|ω}}

[[Category:Greek letters]]
[[Category:Vowel letters]]