Omega

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Omega (majuscule: ZΩ, minuscule: zω; 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 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 in certain dialects such as RP where this word is pronounced [ɹɔː]. It should not be confused with the sound of English so-called "long o" as in ocean, which is either diphthongal [oʊ] or [əʊ] or a close-mid kind of "o" [o], in either case distinctly different from the "long o" sound of Greek omega and closer to the Classical Greek sound represented by ου before this came to be pronounced [u]. 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".^[3]

As Ninhursag's symbol, 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 at the origin of Elder Futhark ᛟ.

[edit] The symbol Ω (majuscule letter)

The upper-case letter Ω is used as a symbol. It is meaning the ending, the last and the finale, as in the book of revelation God is described as the Alpha and the Omega, beginning and end. It is also used often outside its Greek alphabetical context in literature, advertising and other forms of human expression.

• 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. ^[4]
  • The solid angle or the rate of precession in a gyroscope.
  • In particle physics to represent the Omega baryons.
• 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.
• In astronomy (cosmology) Ω refers to the density of the universe, also called the density parameter.
• The symbol of the resistance movement against the Vietnam-era draft
• Year or date of death
• The logo of the popular PlayStation franchise God of War.
• The logo of Omega Watches SA.
• In the fictional world of Star Trek, the Omega symbol is used in conjunction with the Omega Directive.
• In Megaman.EXE, Battle Network 3-6 often the last and hardest form of a boss has the symbol after his/her name.

[edit] The symbol ω (lower case letter)

The minuscule letter ω is used as a symbol:

• In textual criticism, the archetype of a manuscript tradition
• In physics, angular velocity and angular frequency
• In circuit analysis and signal processing to represent natural frequency, related to frequency f by ω = 2πf.
• In Computational fluid dynamics, the specific turbulence dissipation rate
• In mathematics, the first transfinite ordinal number, often identified with the set of natural numbers including 0
• In mathematics, the complex cube roots of 1
• In mathematics, the Wright Omega function
• In mathematics, a generic differential form.
• In mathematics, the elasticity of financial options.
• In number theory, an arithmetic function
• In combinatory logic, the self-application combinator, (λ x. x x)
• In computer science, in notation related to Big O notation, the asymptotically dominant nature of functions
• In astronomy, as a ranking of a star's brightness
• In particle physics to represent the omega meson
• In linguistics, the phonological word
• In biochemistry to denote the carbon atom furthest from the carboxyl group of a fatty acid.
• Used in place of ん in Japanese typing shorthand.
• In relational database theory to represent NULL, a missing or inapplicable value.
• In phonology, for a prosodic (or phonological) word.
• 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.

Marilyn Manson uses omega as one of his themes in his 1999 Glam Rock Album Mechanical Animals

[edit] Notes

1. ^ The Greek Alphabet
2. ^ Herbert Weir Smyth. A Greek Grammar for Colleges. §1
3. ^ 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"
4. ^ Excerpts from the The Unicode Standard, Version 4.0, accessed 11 October 2006