OMEGA

'Omega' (uppercase 'Ω', lowercase 'ω') 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'' (), whereas the Omicron was called ''ou'' ().^[2] The form of the letter derives from a double omicron, which came to be written open at the top.
Phonetically, the Ancient Greek Ω is a long ''o'', similar to the vowel of English ''ocean''. For example, the English ''ocean'', derives from the Greek ''ωκεανός''. It is transcribed ''ō'' or simply ''o''. In Modern Greek Ω also sounds like a long ''o'', though not so clear in everyday speech.
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. 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]
Omega was also adopted into the early Cyrillic alphabet. See omega (Cyrillic) (Ѡ, ѡ). A Raetic variant is at the origin of Elder Futhark ᛟ.

Contents

The symbol Ω (upper case letter)

The symbol ω (lower-case letter)

Notes

The symbol Ω (upper case letter)

The upper-case letter Ω is used as a symbol, it is also used often outside its Greek alphabetical context in literature, advertising and other forms of human expression.

★ 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]

★ In computer science, in notation related to Big O notation to describe the asymptotic behavior of functions. See also Chaitin's constant

★ In mathematics, the Omega constant, a solution of Lambert's W function; or the first uncountable ordinal number (also known as $omega\_1$)

★ Also In mathematics, Omega denotes a 2-d region in calculus, usually corresponding to the domain of a double integral.

★ In statistics, it is used as the symbol for the sample space, or total set of possible outcomes.

★ In physics, the solid angle or the rate of precession in a gyroscope.

★ In particle physics to represent the Omega baryons. A lowercase omega is used for the omega mesons.

★ In combinatory logic, the looping combinator, ''(λ x. x x) (λ x. x x)''

★ In astronomy (cosmology) Ω refers to the density of the universe, also called the density parameter.

The symbol ω (lower-case letter)

The lower-case letter ω is used as a symbol:

★ In textual criticism, the archetype of a manuscript tradition

★ In physics, angular velocity and angular frequency.

★ In mathematics, the first transfinite ordinal number

★ 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 circuit analysis and signal processing to represent natural frequency, related to frequency ''f'' by ω = 2π''f''.

★ 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 ω is used to represent NULL, a missing or inapplicable value.

★ In phonology, for a prosodic (or phonological) word.

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