### Omega (letter)

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Template:Greek Alphabet
**Omega** (

Phonetically, the Ancient Greek Ω is a long open-mid *o* [ɔː], comparable 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.

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 has had little use. See Latin omega.

Omega is also used in Christianity, as a part of the Alpha and Omega metaphor.

## Contents

## The symbol Ω (uppercase letter)

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The upper case letter Ω is used as a symbol:
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- 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 for the ohm sign (U+2126, Ω), but it is only included for backwards compatibility and the Greek uppercase omega character (U+03A9, Ω) is preferred.
^{[5]} - 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 for the ohm sign (U+2126, Ω), but it is only included for backwards compatibility and the Greek uppercase omega character (U+03A9, Ω) is preferred.
- In mathematics and computer science:
- In complex analysis, the Omega constant, a solution of Lambert's W function
- 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,
*(λ x. x x) (λ x. x x)* - In group theory, the omega and agemo subgroups of a
*p*-group, Ω(*G*) and ℧(*G*) - In statistics, it is used as the symbol for the sample space, or total set of possible outcomes.
- In number theory, Ω(
*n*) is the number of prime divisors of*n*. - in notation related to Big O notation to describe the asymptotic behavior of functions.
- Chaitin's constant.

- As part of logo or trademark:
- The logo of Omega Watches SA.
- 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 around Greek mythology.
- The logo of the Heroes of Olympus series, based on Greek mythology.
- the logo of the ultra smurfs in Warhammer 40,000

- Other
- 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
- 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

## The symbol ω (lower case letter)

The minuscule letter ω is used as a symbol:

- Biochemistry and chemistry:
- Denotes the carbon atom furthest from the carboxyl group of a fatty acid.
- In biochemistry, for one of the RNA Polymerase subunits.
- In biochemistry, for the dihedral angle associated with the peptide group, involving the backbone atoms Cα-C'-N-Cα
- In genomics, as a measure of evolution at the protein level (also denoted as d
_{N}/d_{S}or K_{a}/K_{s}ratio).

- Physics
- angular velocity or angular frequency
- 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 natural frequency, related to frequency
*f*by ω = 2π*f* - In astronomy, as a ranking of a star's brightness within a constellation
- In astronomy (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.

- Mathematics:
- The first transfinite ordinal number, often identified with the set of natural numbers including 0 (sometimes written $\backslash omega\_0$)
- In set theory, the first uncountable ordinal number (more commonly written as ω
_{1}) - 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 mathematical/options finance, the elasticity of financial 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

## Character Encodings

- Greek Omega / Coptic Oou

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- Cyrillic Omega

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- Latin / IPA Omega

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- Technical Omega symbols

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- Mathematical Omega

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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 text style.