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"). This name is Byzantine; in Classical Greek, the letter was called ō (ὦ), whereas the Omicron was called ou (οὖ). The form of the lowercase letter derives from a double omicron, which came to be written open at the top.
Phonetically, the Ancient Greek Ω is a long open-mid o [ɔː], similar to the vowel of English raw as pronounced in London or New York. 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, Christ is declared to be the "alpha and omega, the beginning and the end, the first and the last".
As the symbol of the Sumerian goddess Ninhursag, the omega has been depicted in art from around 3000 BC, though more generally from the early second millennium. It appears on some boundary stones on the upper tier, which indicates her importance.
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:
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.
For angular velocity in circular motion
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 mathematics/computer science:
in notation related to Big O notation to describe the asymptotic behavior of functions.
Chaitin's constant.
In mathematics
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 set theory, the first uncountable ordinal number (more commonly written as ω1)
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.
As part of logo or trademark:
The logo of Omega Watches SA.
Part of the Badge of the Supreme Court of the United Kingdom.
In fictional worlds
In the fictional world of Star Trek, the Omega symbol is used in conjunction with the Omega Directive.
The logo of the popular PlayStation franchise God of War.
As the symbol for the Sons of Orar Chapter and ,if turned upside down, the symbol for the Ultramarine Chapter both of the Space Marines (Warhammer 40,000) , in the fictional universe Warhammer 40,000
Other
The symbol of the resistance movement against the Vietnam-era draft
Year or date of death
The symbol ω (lower case letter)
The minuscule letter ω is used as a symbol: Biochemisty 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 dN/dS or Ka/Ks ratio).
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
The complex cube roots of 1
The Wright Omega function
A generic differential form.
In number theory, an arithmetic function
In combinatory logic, the self-application combinator, (λ x. x x)
In mathematical finance, the elasticity of financial options.
Physics:
angular velocity or angular frequency
Computational fluid dynamics : the specific turbulence dissipation rate
In circuit analysis and signal processing to represent natural frequency, related to frequency f by ω = 2πf.
In astronomy, as a ranking of a star's brightness
In particle physics to represent the omega meson
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 phonology, for a prosodic (or phonological) word.
In sociology, used to refer to the lowest ranking member of a group.
Translation
The word "Omega" occurs as such in the following languages: English, Asturian, Catalan, Czech, Welsh, German, Basque, Scottish Gaelic, Galician, Croatian, Indonesian, Swahili, Kurdish, Latin, Malay, Norwegian (Bokmål), Norwegian (Nynorsk), Low Saxon, Polish, Scots, Simple English, Slovenian, Serbo-Croatian, Swedish.
Translation(s) in other languages: Alemannic: Ω, Arabic: أوميغا, Assyrian Neo-Aramaic: Ω, Bengali: ওমেগা, Breton: Omega (lizherenn), Bulgarian: Омега, Danish: Omega (bogstav), Greek: Ωμέγα, Spanish: Ω, Esperanto: Omego, Persian: امگا, French: Oméga, Korean: Ω, Icelandic: Ómega, Italian: Omega (lettera), Hebrew: אומגה, Georgian: ომეგა (ასო), Haitian: Ω, Lithuanian: Omega (raidė), Hungarian: Ómega, Dutch: Omega (letter), Japanese: Ω, Portuguese: Ω, Russian: Омега (буква), Slovak: Ómega, Finnish: Oomega, Thai: โอเมกา, Turkish: Omega (alfabe), Ukrainian: Омега (літера), Wu: Ω, Cantonese: Ω, Chinese: Ω.
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