Omega: Difference between revisions

Content deleted Content added

Inline

Revision as of 02:08, 10 December 2007

This article contains special characters. Without proper rendering support, you may see question marks, boxes, or other symbols.

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 (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. 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]

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.

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 $\omega _{1}$ )
In mathematics, Omega denotes Chaitin's constant.
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.
Year or date of death

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 = 2πf.
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.
In biochemistry, for one of the RNA Polymerase subunits.

Notes

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

[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

[1]

[2]

[3]

[4]

@@ Line 11: / Line 11: @@
 Omega was also adopted into the [[early Cyrillic alphabet]].  See [[omega (Cyrillic)]] (Ѡ, ѡ). A [[Raetic alphabet|Raetic]] variant is at the origin of [[Elder Futhark]] [[ᛟ]].
+== 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 (unit)|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 (unit)|siemens]] with symbol S) used for electrical conductance. [[Unicode]] has a separate code point for the [[Ohm (unit)|ohm]] sign (U+2126, &#x2126;), but it is only included for backwards compatibility and the Greek uppercase omega character (U+03A9, Ω) is preferred. <ref>Excerpts from the ''[http://www.unicode.org/versions/Unicode4.0.0/ch07.pdf#search=%22character%20U%2B2126%20maps%20OR%20map%20OR%20mapping%22 The Unicode Standard, Version 4.0]'', accessed [[11 October]] [[2006]]</ref>
+* In [[computer science]], in notation related to [[Big O notation]] to describe the [[asymptotic behavior]] of [[function (mathematics)|function]]s. See also [[Chaitin's constant]]
+* In [[mathematics]], the [[Omega constant]], a solution of [[Lambert's W function]]; or the first [[uncountable set|uncountable]] [[ordinal number]] (also known as <math>\omega_1</math>)
+* In [[mathematics]], [[Omega]] denotes [[Chaitin's constant]].
+*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 baryon]]s. A lowercase omega is used for the [[omega meson]]s.
+* In [[combinatory logic]], the looping combinator, ''(λ x. x x) (λ x. x x)''
+* In [[astronomy]] ([[physical cosmology|cosmology]]) Ω refers to the density of the universe, also called the [[density parameter]].
+* Year or date of death
 == The symbol ω (lower-case letter) ==