# Omega

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**Omega** (US: /oʊˈmeɪɡə, -ˈmɛɡə, -ˈmiːɡə/, UK: /ˈoʊmɪɡə/;^{[1]} 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" (*ō mega*, mega meaning "great"), as opposed to omicron, which means "little O" (*o mikron*, micron meaning "little").^{[2]}

In phonetic terms, the Ancient Greek Ω represented a long open-mid back rounded vowel IPA: [ɔː], 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: [o] , and the digraph *ου* which represented the long close-mid back rounded vowel IPA: [oː]. In Modern Greek, both omega and omicron represent the mid back rounded vowel IPA: [o̞] or IPA: [ɔ̝]. 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

[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 a long 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 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 /o/.^{[3]}

The name Ωμέγα is Byzantine; in Classical Greek, the letter was called *ō* (ὦ) (pronounced /ɔ̂ː/), whereas the omicron was called *ou* (οὖ) (pronounced /ôː/).^{[4]} The modern lowercase shape goes back to the uncial form , 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 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 sparce use (see Latin omega).

## The symbol Ω (uppercase letter)

[edit]The uppercase letter Ω is used as a symbol:

- In chemistry:
- For oxygen-18, a natural, stable isotope of oxygen
^{[6]} - 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.

- For oxygen-18, a natural, stable isotope of oxygen
- In physics:
- 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 with symbol S) used for electrical conductance. Unicode has a separate code point U+2126 Ω OHM SIGN (HTML entity
`Ω`

), but it is included only for backward compatibility, and the canonically equivalent code point U+03A9 Ω GREEK CAPITAL LETTER OMEGA (`Ω`

) is preferred.^{[7]} - In statistical mechanics, Ω refers to the multiplicity (number of microstates) in a system.
- The solid angle or the rate of precession in a gyroscope
- In particle physics to represent the Omega baryons
- In astronomy (cosmology), Ω refers to the 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.

- 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 with symbol S) used for electrical conductance. Unicode has a separate code point U+2126 Ω OHM SIGN (HTML entity
- In mathematics and computer science:
- In complex analysis, the Omega constant, a solution of Lambert's W function
- 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
- In number theory, Ω(
*n*) is the number of prime divisors of*n*(counting multiplicity).^{[8]} - In notation related to Big O notation to describe the asymptotic behavior of functions.
- Chaitin's constant.
- In set theory, the first infinite ordinal number, ω
- In set theory, the first uncountable ordinal number, ω
_{1}or Ω

- As part of logo or trademark:
- The logo of Omega Watches SA
- Part of the original Pioneer logo
- Part of the Badge of the Supreme Court of the United Kingdom
- Part of the mission patch for STS-135, as it was the last mission 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

- 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
- 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.
^{[10]} - It's used along with Alpha in the Alpha and Omega, a Christian symbol.

## The symbol ω (lowercase letter)

[edit]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
- 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 = 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 omega meson

- 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 )
- In set theory, ω
_{1}is the first uncountable ordinal number^{[11]}(also sometimes written as Ω) - A primitive root of unity, like the complex cube roots of 1
- The Wright Omega function
- A generic differential form
- In number theory, ω(
*n*) is the number of distinct prime divisors of*n* - In number theory, an arithmetic function
- In combinatory logic, the self-application combinator,
*(λ x. x x)* - In triangle geometry, a Brocard angle
- Clique number in Graph theory

- 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
^{[12]} - In shift_JIS art, used to represent the cat's mouth. (e.g. (´･ω･`) ｼｮﾎﾞｰﾝ)
- In actuarial sciences, used to represent the maximum life span that characterizes a mortality 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 |

^{[13]}

### 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 |

Preview | ɷ | Ꞷ | ꞷ | | ||||
---|---|---|---|---|---|---|---|---|

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. ISBN 978-1-4058-8118-0.**^**"The Greek Alphabet".- ^
^{a}^{b}Anne 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 from the original (PDF) on 23 September 2015. Retrieved 8 May 2017.**^**Excerpts from*The Unicode Standard, Version 4.0*. Retrieved 11 October 2006.**^**Weisstein, Eric W. "Prime Factor".*mathworld.wolfram.com*. Retrieved 12 August 2020.**^**"Desde la Revolución hasta el 2020".*Gobierno de Aguascalientes*. Retrieved 7 August 2024....su fachada representa a una omega que simboliza el final de la vida.

**^**http://www.substancenews.net/articles.php?page=6592**^**"first uncountable ordinal in nLab".*NCatLab.org*. Retrieved 12 August 2020.**^**"Definition of Omega Male, BuzzWord from Macmillan Dictionary".*macmillandictionary.com*. Retrieved 10 February 2021.**^**Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)

## External links

[edit]- Media related to Omega (letter) at Wikimedia Commons
- The dictionary definition of
*ω*at Wiktionary