Omega

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'''Omega''' ([[capital letter|majuscule]]: '''Ω''', [[lower case|minuscule]]: '''ω'''; [[Ancient Greek|Greek]] Ωμέγα) is the 24th and last letter of the [[Greek alphabet]]. In the [[Greek numerals|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"). This name is [[Medieval Greek|Byzantine]]; in [[Ancient Greek|Classical Greek]], the letter was called ''ō'' (ὦ), whereas the [[Omicron]] was called ''ou'' (οὖ).
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[[Image:omega.png|thumb|150px|Omega]]
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1. The last letter of the [[Greek alphabet]]. See [[Alpha]].
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'''Omega''' ([[capital letter|majuscule]]: '''Ω''', [[lower case|minuscule]]: '''ω'''; [[Ancient Greek|Greek]] Ωμέγα) is the 24th and last letter of the [[Greek alphabet]]. In the [[Greek numerals|Greek numeric system]], it has a value of 800. The word literally means "great&nbsp;O" (''ō mega'', mega meaning 'great'), as opposed to [[Omicron]], which means "little&nbsp;O" (''o mikron'', micron meaning "little").<sup>[1]</sup> This name is [[Medieval Greek|Byzantine]]; in [[Ancient Greek|Classical Greek]], the letter was called ''ō'' (ὦ), whereas the Omicron was called ''ou'' (οὖ).<sup>[2]</sup> The form of the uppercase letter derives from that of an Omicron (Ο) broken up at the side ([[Image:Greek Omega 09.png|x16px]]), with the edges subsequently turned outwards ([[Image:Greek Omega 05.png|x16px]], [[Image:Greek Omega 03.png|x16px]], [[Image:Greek Omega 07.png|x16px]]).<sup>[3]</sup> The modern lowercase shape goes back to the [[uncial]] form [[Image: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 ([[Image:Greek Omega 08.png|x16px]]) that had its edges curved even further upwards.<sup>[4]</sup>
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2. The last; the end; hence, death.
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Phonetically, the Ancient Greek Ω is a [[vowel length|long]] [[open-mid back unrounded vowel|open-mid ''o'']] [ɔː], equal to the vowel of British English ''raw''. In [[Modern Greek]] Ω represents the same sound as omicron. The letter omega is [[transcription (linguistics)|transcribed]] ''ō'' or simply ''o''.
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Omega (the last letter of the Greek alphabet) 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. In the New Testament book of Revelation, God is declared to be the "[[Alpha and Omega|alpha and omega]], the beginning and the end, the first and the last".<sup>[5]</sup>
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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]].
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== The symbol Ω (majuscule letter) ==
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The [[majuscule]] letter Ω is used as a symbol:
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* In [[chemistry]]:
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** For [[Oxygen-18]] a natural, stable isotope of oxygen
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* In [[physics]]:
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** 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 (unit)|siemens]] with symbol S) used for electrical conductance. [[Unicode]] has a separate code point for the [[Ohm (unit)|ohm]] sign (U+2126, Ω), but it is only included for backwards compatibility and the Greek uppercase omega character (U+03A9, Ω) is preferred.<sup>[6]</sup>
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** In [[statistical mechanics]] Ω refers to the multiplicity (number of microstates) in a system.
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** The [[solid angle]] or the rate of precession in a gyroscope.
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** In [[particle physics]] to represent the [[Omega baryon]]s.
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** In [[astronomy]] ([[physical cosmology|cosmology]]) Ω refers to the density of the universe, also called the [[density parameter]].
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** In astronomy ([[orbital mechanics]]), Ω refers to the [[longitude of the ascending node]] of an orbit
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*In [[mathematics]] / [[computer science]]:
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** in notation related to [[Big O notation]] to describe the [[asymptotic behavior]] of [[function (mathematics)|function]]s.
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** [[Chaitin's constant]].
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* In mathematics
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** In [[complex analysis]], the [[Omega constant]], a solution of [[Lambert's W function]]
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** A variable for a 2-dimensional region in calculus, usually corresponding to the domain of a double integral.
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** In [[set theory]],  the [[first uncountable ordinal|first uncountable ordinal number]] (more commonly written as ω<sub>1</sub>)
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** In [[topos theory]], the (codomain of the) [[subobject classifier]] of an elementary topos.
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** In [[combinatory logic]], the looping combinator, ''(λ x. x x) (λ x. x x)''
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** In [[group theory]], the [[omega and agemo subgroup]]s of a ''p''-group, Ω(''G'') and ℧(''G'')
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** In [[statistics]], it is used as the symbol for the [[sample space]], or total set of possible outcomes.
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*As part of logo or trademark:
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** The logo of [[Omega Watches]] SA.
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** Part of the [[Supreme Court of the United Kingdom#Badge|Badge of the Supreme Court]] of the United Kingdom.
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* In fictional worlds:
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** In the fictional world of [[Star Trek]], the Omega symbol is used in conjunction with the [[Omega Directive]].
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** As the logo of the popular [[PlayStation]] franchise [[God of War (series)|God of War]], a game based around Greek mythology.
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** In the fictional universe [[Warhammer 40,000]], the symbol for the Sons of Orar Chapter and, if turned upside down, the symbol for the Ultramarine Chapter of the [[Space Marines (Warhammer 40,000)]].
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** In the popular web series [[Red vs Blue]] the Blood Gulch Chronicles Omega (or O'Malley) is Freelancer Tex's AI implant and the main antagonist of the Blood Gulch Chronicles
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** In Locke and Key, the antagonist, Dodge, is searching for the Omega Key.
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** In the [[X-Men (film series)|X-Men Movies]] the symbol is used in tattoos by [[Mutant (Marvel Comics)|mutants]] (particularly those who join the [[Brotherhood of Mutants]]) to publicly announce their mutant status.
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** In the [[Caprica (TV series)|Caprica]] television series, Tauron's use the symbol to [http://en.battlestarwiki.org/wiki/Sam_Adama represent marriage].
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** In the [[EarthBound (series)|EarthBound]] video game series, Ω denotes the most powerful incarnation of a psychic attack.
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** In the [[Sonic the Hedgehog series]] there is a robot named [[E-123 Omega]].
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*Other
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** The [[Marilyn Manson]] album [[Mechanical Animals]] has false band within the album called [[Omēga]] and the Mechanical Animals
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** The symbol of the resistance movement against the Vietnam-era draft
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** Year or date of death
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** Used to refer to the lowest-ranked wolf in a pack
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** Can be referred to the end of death or even time. The name of the end.
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** As a tattoo, to symbolise marriage in monogamy. The bottom of the symbol is sealed should the partner die.
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** Was part of the [[Pioneer Corporation|Pioneer Corporation's]] logo from 1970-1995.
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== The symbol ω (minuscule letter) ==
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The [[lower case|minuscule]] letter ω is used as a symbol:
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*Biochemistry and chemistry:
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** Denotes the carbon atom furthest from the [[carboxyl group]] of a [[fatty acid]].
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** In [[biochemistry]], for one of the [[RNA]] [[Polymerase]] subunits.
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** In biochemistry, for the dihedral angle associated with the peptide group, involving the backbone atoms Cα-C'-N-Cα
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** In [[genomics]],  as a measure of [[evolution]] at the protein level (also denoted as d<sub>N</sub>/d<sub>S</sub> or [[Ka/Ks ratio|K<sub>a</sub>/K<sub>s</sub> ratio]]).
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*Physics:
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** For [[angular velocity]] in circular motion
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*Computer science:
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** In notation related to [[Big O notation]], the [[asymptotical dominance|asymptotically dominant]] nature of [[function (mathematics)|function]]s
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** In [[relational database]] theory to represent [[Null (SQL)|NULL]], a missing or inapplicable value.
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*Mathematics:
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** The first [[transfinite number|transfinite]] [[ordinal number]], often identified with the set of natural numbers including 0
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** The complex [[roots of unity|cube roots of 1]]
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** The [[Wright Omega Function|Wright Omega function]]
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** A generic [[differential form]]
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** In [[number theory]], an [[arithmetic function]]
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** In [[combinatory logic]], the self-application combinator, ''(λ x. x x)''
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** In mathematical/options finance, the elasticity of financial options
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** In analytical investment management, the [[tracking error]] of an investment manager
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** Also referred to as wubula by high school math teams in the US
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*Physics:
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**[[angular velocity]] or [[angular frequency]]
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**[[Computational fluid dynamics]] : the specific turbulence dissipation rate
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** In [[circuit analysis]] and [[signal processing]] to represent natural frequency, related to [[frequency]] ''f'' by ω = 2π''f''
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** In [[astronomy]], as a ranking of a star's brightness
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** In astronomy ([[orbital mechanics]]), as designation of the [[argument of periapsis]] of an orbit
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** In [[particle physics]] to represent the [[Meson|omega meson]]
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*Other:
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** Used in place of [[ん]] in Japanese typing shorthand.
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** In [[linguistics]], the [[phonological word]]
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** In [[textual criticism]], the [[archetype]] of a manuscript tradition
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** In [[sociology]], used to refer to the lowest ranking member of a group
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== Notes ==
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* 1. [http://www.quinapalus.com/gr0.1.html The Greek Alphabet]
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* 2. Herbert Weir Smyth. A Greek Grammar for Colleges. §1
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* 3. Anne Jeffery ([[1961]]), The local scripts of archaic Greece, p.37–38.
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* 4. Edward M. Thompson (1912), Introduction to Greek and Latin paleography, Oxford: Clarendon. p.144
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* 5. [[Revelation 22:13]], [[KJV]], and see also [[Revelation 1:8|1:8]], Greek ἐγὼ τὸ ἄλφα καὶ τὸ ὦ, ὁ πρῶτος καὶ ὁ ἔσχατος, ἡ ἀρχὴ καὶ τὸ τέλος. Or in [[Revelation 1:8]] as seen in the [[Latin Vulgate]] Bible, the [[Greek]] is shown, surrounded by [[Latin]]: "ego sum α et ω principium et finis dicit Dominus Deus qui est et qui erat et qui venturus est Omnipotens"
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* 6. Excerpts from The Unicode Standard, Version 4.0. Retrieved 11 October 2006.
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[[Category:Greek letters]]
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[[Category:Vowel letters]]

Revision as of 03:58, 10 April 2011

Omega
Omega

Omega (majuscule: Ω, minuscule: 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] This name is Byzantine; in Classical Greek, the letter was called ō (ὦ), whereas the Omicron was called ou (οὖ).[2] The form of the uppercase letter derives from that of an Omicron (Ο) broken up at the side (), with the edges subsequently turned outwards (, , ).[3] The modern lowercase shape goes back to the uncial form Image:Greek uncial Omega.svg, 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 upwards.[4]

Phonetically, the Ancient Greek Ω is a long open-mid o [ɔː], equal to the vowel of British English raw. In Modern Greek Ω represents the same sound as omicron. The letter omega is transcribed ō or simply o.

Omega (the last letter of the Greek alphabet) 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. In the New Testament book of Revelation, God is declared to be the "alpha and omega, the beginning and the end, the first and the last".[5]

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.

The symbol Ω (majuscule letter)

The majuscule letter Ω is used as a symbol:

  • Other
    • The Marilyn Manson album Mechanical Animals has false band within the album called Omēga and the Mechanical Animals
    • The symbol of the resistance movement against the Vietnam-era draft
    • Year or date of death
    • Used to refer to the lowest-ranked wolf in a pack
    • Can be referred to the end of death or even time. The name of the end.
    • As a tattoo, to symbolise marriage in monogamy. The bottom of the symbol is sealed should the partner die.
    • Was part of the Pioneer Corporation's logo from 1970-1995.

The symbol ω (minuscule letter)

The minuscule letter ω is used as a symbol:

Notes

  • 1. The Greek Alphabet
  • 2. Herbert Weir Smyth. A Greek Grammar for Colleges. §1
  • 3. Anne Jeffery (1961), The local scripts of archaic Greece, p.37–38.
  • 4. Edward M. Thompson (1912), Introduction to Greek and Latin paleography, Oxford: Clarendon. p.144
  • 5. Revelation 22:13, KJV, and see also 1:8, Greek ἐγὼ τὸ ἄλφα καὶ τὸ ὦ, ὁ πρῶτος καὶ ὁ ἔσχατος, ἡ ἀρχὴ καὶ τὸ τέλος. Or in Revelation 1:8 as seen in the Latin Vulgate Bible, the Greek is shown, surrounded by Latin: "ego sum α et ω principium et finis dicit Dominus Deus qui est et qui erat et qui venturus est Omnipotens"
  • 6. Excerpts from The Unicode Standard, Version 4.0. Retrieved 11 October 2006.
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