Omega
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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" (ō mega,mega meaning "great" ), as opposed toomicron,which means "little O" (o mikron,micron meaning "little" ).[2]
Inphoneticterms, the Ancient Greek Ω represented alongopen-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 thelongclose-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[edit]
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 alongopen-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 Futharkᛟ.
Omega was also adopted into the Latin alphabet, as a letter of the 1982 revision to theAfrican reference alphabet.It's in sparce use (seeLatin omega).
The symbol Ω (uppercase letter)[edit]
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
Ω
), 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 density of the universe, also called thedensity parameter.
- In astronomy (orbital mechanics), Ω refers to thelongitude of the ascending nodeof an orbit.
- 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
- 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 infinite ordinal number,ω
- Inset theory,thefirst uncountable ordinal number,ω1or Ω
- 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
- 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.[9]
- It's used along withAlphain theAlpha and Omega,a Christian symbol.
The symbol ω (lowercase letter)[edit]
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 dN/dSorKa/Ksratio)
- 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 smallesttransfiniteordinal number,often identified with the set of natural numbers including 0 (sometimes written)
- Inset theory,ω1is thefirst uncountable ordinal number[10](also sometimes written as Ω)
- 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[11]
- Inshift_JIS art,used to represent the cat's mouth. (e.g.(´・ω・`) ショボーン)
- Inactuarial sciences,used to represent the maximum life span that characterizes amortality table
Character encodings[edit]
Greek omega/Coptic oou[edit]
Preview | Ω | ω | Ⲱ | ⲱ | ||||
---|---|---|---|---|---|---|---|---|
Unicode name | GREEK CAPITAL LETTER OMEGA | GREEK SMALL LETTER OMEGA | COPTIC CAPITAL LETTER OOU | COPTIC SMALL LETTER OOU | ||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex |
Unicode | 937 | U+03A9 | 969 | U+03C9 | 11440 | U+2CB0 | 11441 | U+2CB1 |
UTF-8 | 206 169 | CE A9 | 207 137 | CF 89 | 226 178 176 | E2 B2 B0 | 226 178 177 | E2 B2 B1 |
Numeric character reference | Ω |
Ω |
ω |
ω |
Ⲱ |
Ⲱ |
ⲱ |
ⲱ |
Named character reference | Ω, Ω | ω | ||||||
DOS Greek | 151 | 97 | 224 | E0 | ||||
DOS Greek-2 | 213 | D5 | 250 | FA | ||||
Windows 1253 | 217 | D9 | 249 | F9 | ||||
TeX | \Omega | \omega |
Cyrillic omega[edit]
Preview | Ѡ | ѡ | ꙻ | |||
---|---|---|---|---|---|---|
Unicode name | CYRILLIC CAPITAL LETTER OMEGA | CYRILLIC SMALL LETTER OMEGA | COMBINING CYRILLIC LETTER OMEGA | |||
Encodings | decimal | hex | dec | hex | dec | hex |
Unicode | 1120 | U+0460 | 1121 | U+0461 | 42619 | U+A67B |
UTF-8 | 209 160 | D1 A0 | 209 161 | D1 A1 | 234 153 187 | EA 99 BB |
Numeric character reference | Ѡ |
Ѡ |
ѡ |
ѡ |
ꙻ |
ꙻ |
Preview | Ѻ | ѻ | Ꙍ | ꙍ | ||||
---|---|---|---|---|---|---|---|---|
Unicode name | CYRILLIC CAPITAL LETTER ROUND OMEGA | CYRILLIC SMALL LETTER ROUND OMEGA | CYRILLIC CAPITAL LETTER BROAD OMEGA | CYRILLIC SMALL LETTER BROAD OMEGA | ||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex |
Unicode | 1146 | U+047A | 1147 | U+047B | 42572 | U+A64C | 42573 | U+A64D |
UTF-8 | 209 186 | D1 BA | 209 187 | D1 BB | 234 153 140 | EA 99 8C | 234 153 141 | EA 99 8D |
Numeric character reference | Ѻ |
Ѻ |
ѻ |
ѻ |
Ꙍ |
Ꙍ |
ꙍ |
ꙍ |
Latin/IPAomega[edit]
Preview | ɷ | Ꞷ | ꞷ | 𐞤 | ||||
---|---|---|---|---|---|---|---|---|
Unicode name | LATIN SMALL LETTER CLOSED OMEGA | LATIN CAPITAL LETTER OMEGA | LATIN SMALL LETTER OMEGA | MODIFIER LETTER SMALL CLOSED OMEGA | ||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex |
Unicode | 631 | U+0277 | 42934 | U+A7B6 | 42935 | U+A7B7 | 67492 | U+107A4 |
UTF-8 | 201 183 | C9 B7 | 234 158 182 | EA 9E B6 | 234 158 183 | EA 9E B7 | 240 144 158 164 | F0 90 9E A4 |
UTF-16 | 631 | 0277 | 42934 | A7B6 | 42935 | A7B7 | 55297 57252 | D801 DFA4 |
Numeric character reference | ɷ |
ɷ |
Ꞷ |
Ꞷ |
ꞷ |
ꞷ |
𐞤 |
𐞤 |
Technical omega symbols[edit]
Preview | ⍵ | ⍹ | Ω | ℧ | ||||
---|---|---|---|---|---|---|---|---|
Unicode name | APL FUNCTIONAL SYMBOL OMEGA | APL FUNCTIONAL SYMBOL OMEGA UNDERBAR | OHM SIGN | INVERTED OHM SIGN | ||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex |
Unicode | 9077 | U+2375 | 9081 | U+2379 | 8486 | U+2126 | 8487 | U+2127 |
UTF-8 | 226 141 181 | E2 8D B5 | 226 141 185 | E2 8D B9 | 226 132 166 | E2 84 A6 | 226 132 167 | E2 84 A7 |
Numeric character reference | ⍵ |
⍵ |
⍹ |
⍹ |
Ω |
Ω |
℧ |
℧ |
Named character reference | ℧ |
Mathematical omega[edit]
Preview | 𝛀 | 𝛚 | 𝛺 | 𝜔 | 𝜴 | 𝝎 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Unicode name | MATHEMATICAL 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 | ||||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex | dec | hex | dec | hex |
Unicode | 120512 | U+1D6C0 | 120538 | U+1D6DA | 120570 | U+1D6FA | 120596 | U+1D714 | 120628 | U+1D734 | 120654 | U+1D74E |
UTF-8 | 240 157 155 128 | F0 9D 9B 80 | 240 157 155 154 | F0 9D 9B 9A | 240 157 155 186 | F0 9D 9B BA | 240 157 156 148 | F0 9D 9C 94 | 240 157 156 180 | F0 9D 9C B4 | 240 157 157 142 | F0 9D 9D 8E |
UTF-16 | 55349 57024 | D835 DEC0 | 55349 57050 | D835 DEDA | 55349 57082 | D835 DEFA | 55349 57108 | D835 DF14 | 55349 57140 | D835 DF34 | 55349 57166 | D835 DF4E |
Numeric character reference | 𝛀 |
𝛀 |
𝛚 |
𝛚 |
𝛺 |
𝛺 |
𝜔 |
𝜔 |
𝜴 |
𝜴 |
𝝎 |
𝝎 |
Preview | 𝝮 | 𝞈 | 𝞨 | 𝟂 | ||||
---|---|---|---|---|---|---|---|---|
Unicode name | MATHEMATICAL 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 | ||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex |
Unicode | 120686 | U+1D76E | 120712 | U+1D788 | 120744 | U+1D7A8 | 120770 | U+1D7C2 |
UTF-8 | 240 157 157 174 | F0 9D 9D AE | 240 157 158 136 | F0 9D 9E 88 | 240 157 158 168 | F0 9D 9E A8 | 240 157 159 130 | F0 9D 9F 82 |
UTF-16 | 55349 57198 | D835 DF6E | 55349 57224 | D835 DF88 | 55349 57256 | D835 DFA8 | 55349 57282 | D835 DFC2 |
Numeric character reference | 𝝮 |
𝝮 |
𝞈 |
𝞈 |
𝞨 |
𝞨 |
𝟂 |
𝟂 |
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.
References[edit]
- ^Wells, John C.(2008). "omega".Longman Pronunciation Dictionary(3rd ed.). Longman.ISBN978-1-4058-8118-0.
- ^"The Greek Alphabet".
- ^abAnne 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.
- ^http://www.substancenews.net/articles.php?page=6592
- ^"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[edit]
Media related toOmega (letter)at Wikimedia Commons
The dictionary definition ofωat Wiktionary