Omega (;
capital
Capital may refer to:
Common uses
* Capital city, a municipality of primary status
** List of national capital cities
* Capital letter, an upper-case letter Economics and social sciences
* Capital (economics), the durable produced goods used fo ...
: Ω,
lowercase: ω;
Ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic pe ...
ὦ, later ὦ μέγα,
Modern Greek
Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the dialects of the Greek language spoken in the modern era, including the official standardized form of the ...
ωμέγα) is the twenty-fourth and final letter in the
Greek alphabet
The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BCE. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as ...
. In the
Greek numeric system/
isopsephy (
gematria), it has a value of 800. The word literally means "great O" (''ō mega'', mega meaning "great"), as opposed to
omicron
Omicron (; uppercase Ο, lowercase ο, ell, όμικρον) is the 15th letter of the Greek alphabet. This letter is derived from the Phoenician letter ayin: . In classical Greek, omicron represented the close-mid back rounded vowel in contr ...
, which means "little O" (''o mikron'', micron meaning "little").
In
phonetic
Phonetics is a branch of linguistics that studies how humans produce and perceive sounds, or in the case of sign languages, the equivalent aspects of sign. Linguists who specialize in studying the physical properties of speech are phoneticians. ...
terms, the Ancient Greek Ω represented a
long
Long may refer to:
Measurement
* Long, characteristic of something of great duration
* Long, characteristic of something of great length
* Longitude (abbreviation: long.), a geographic coordinate
* Longa (music), note value in early music mensu ...
open-mid back rounded vowel , comparable to the "aw" of the
English
English usually refers to:
* English language
* English people
English may also refer to:
Peoples, culture, and language
* ''English'', an adjective for something of, from, or related to England
** English national ...
word ''raw'' in dialects without the
cot–caught merger, in contrast to
omicron
Omicron (; uppercase Ο, lowercase ο, ell, όμικρον) is the 15th letter of the Greek alphabet. This letter is derived from the Phoenician letter ayin: . In classical Greek, omicron represented the close-mid back rounded vowel in contr ...
which represented the
close-mid back rounded vowel , and the
digraph ''ου'' which represented the
long
Long may refer to:
Measurement
* Long, characteristic of something of great duration
* Long, characteristic of something of great length
* Longitude (abbreviation: long.), a geographic coordinate
* Longa (music), note value in early music mensu ...
close-mid back rounded vowel . In
Modern Greek
Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the dialects of the Greek language spoken in the modern era, including the official standardized form of the ...
, both omega and omicron represent the
mid back rounded vowel or . The letter omega is
transliterated into a
Latin-script alphabet as ''ō'' or simply ''o''.
As the final letter in the Greek alphabet, omega is often used to denote the last, the end, or the ultimate limit of a
set
Set, The Set, SET or SETS may refer to:
Science, technology, and mathematics Mathematics
*Set (mathematics), a collection of elements
*Category of sets, the category whose objects and morphisms are sets and total functions, respectively
Electro ...
, in contrast to
alpha
Alpha (uppercase , lowercase ; grc, ἄλφα, ''álpha'', or ell, άλφα, álfa) is the first letter of the Greek alphabet. In the system of Greek numerals, it has a value of one. Alpha is derived from the Phoenician letter aleph , whi ...
, the first letter of the Greek alphabet; see
Alpha and Omega.
History
Ω was not part of the early (8th century BC)
Greek alphabets. It was introduced in the late 7th century BC in the Ionian cities of Asia Minor to denote a
long
Long may refer to:
Measurement
* Long, characteristic of something of great duration
* Long, characteristic of something of great length
* Longitude (abbreviation: long.), a geographic coordinate
* Longa (music), note value in early music mensu ...
open-mid back rounded vowel . It is a variant of omicron (Ο), broken up at the side (
), with the edges subsequently turned outward (, , , ).
[Anne Jeffery (1961), ''The local scripts of archaic Greece'', p.37–38.]
The Dorian city of
Knidos as well as a few Aegean islands, namely
Paros,
Thasos
Thasos or Thassos ( el, Θάσος, ''Thásos'') is a Greek island in the North Aegean Sea. It is the northernmost major Greek island, and 12th largest by area.
The island has an area of and a population of about 13,000. It forms a separate r ...
and
Melos, chose the exact opposite innovation, using a broken-up circle for the short and a closed circle for the long .
[
The name Ωμέγα is ]Byzantine
The Byzantine Empire, also referred to as the Eastern Roman Empire or Byzantium, was the continuation of the Roman Empire primarily in its eastern provinces during Late Antiquity and the Middle Ages, when its capital city was Constantinopl ...
; in Classical Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic pe ...
, the letter was called ''ō'' () (pronounced /ɔ̂ː/), whereas the omicron was called ''ou'' () (pronounced /ôː/).
The modern lowercase shape goes back to the uncial form , a form that developed during the 3rd century BC in ancient handwriting on papyrus, from a flattened-out form of the letter () that had its edges curved even further upward.
In addition to the Greek alphabet, Omega was also adopted into the early Cyrillic alphabet. See Cyrillic omega (Ѡ, ѡ). A Raetic
Rhaetic or Raetic (), also known as Rhaetian, was a language spoken in the ancient region of Rhaetia in the eastern Alps in pre-Roman and Roman times. It is documented by around 280 texts dated from the 5th up until the 1st century BC, which wer ...
variant is conjectured to be at the origin or parallel evolution of the Elder Futhark ᛟ
Othala (), also known as odal and ēðel, is a rune that represents the ''o'' and ''œ'' phonemes in the Elder Futhark and the Anglo-Saxon Futhorc writing systems respectively. Its name is derived from the reconstructed Proto-Germanic *''ōþ ...
.
Omega was also adopted into the Latin alphabet, as a letter of the 1982 revision to the African reference alphabet
An African reference alphabet was first proposed in 1978 by a UNESCO-organized conference held in Niamey, Niger, and the proposed alphabet was revised in 1982. The conference recommended the use of single letters for a sound (that is, a phonem ...
. It has had little use. See Latin omega
Latin omega, or simply omega, is an additional letter of the Latin alphabet, based on the lowercase of the Greek letter omega . It was included as a Latin letter in the Mann and Dalby 1982 revision of the African reference alphabet and has been u ...
.
The symbol Ω (uppercase letter)
The uppercase letter Ω is used as a symbol:
* In chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, proper ...
:
** For oxygen-18, a natural, stable isotope of oxygen.
* In physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
:
** For ohm
Ohm (symbol Ω) is a unit of electrical resistance named after Georg Ohm.
Ohm or OHM may also refer to:
People
* Georg Ohm (1789–1854), German physicist and namesake of the term ''ohm''
* Germán Ohm (born 1936), Mexican boxer
* Jörg Ohm (bor ...
– SI unit of electrical resistance; formerly also used upside down (℧) to represent mho
The siemens (symbol: S) is the unit of electric conductance, electric susceptance, and electric admittance in the International System of Units (SI). Conductance, susceptance, and admittance are the reciprocals of resistance, reactance, and ...
, 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 included only for backward compatibility, and the Greek uppercase omega character (U+03A9, Ω) is preferred.
** 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
The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity. They were first derived by Alexander Friedmann ...
.
** In astronomy (orbital mechanics), Ω refers to the longitude of the ascending node of an orbit.
*In mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
and computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
:
** In complex analysis, the Omega constant
The omega constant is a mathematical constant defined as the unique real number that satisfies the equation
:\Omega e^\Omega = 1.
It is the value of , where is Lambert's function. The name is derived from the alternate name for Lambert's fu ...
, a solution of Lambert's W function
** In differential geometry, the space of differential form
In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many application ...
s on a manifold (of a certain degree, usually with a superscript).
** 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, ''(S I I (S I I))''
** In group theory, the omega and agemo subgroup
In mathematics, or more specifically group theory, the omega and agemo subgroups described the so-called "power structure" of a finite ''p''-group. They were introduced in where they were used to describe a class of finite ''p''-groups whose st ...
s of a ''p''-group, Ω(''G'') and ℧(''G'')
** In group theory, Cayley's Ω process as a partial differential operator.
** 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'' (counting multiplicity).
** In notation related to Big O notation to describe the asymptotic behavior of functions.
** Chaitin's constant.
**In set theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concern ...
, the first infinite ordinal number, ω
** In set theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concern ...
, the first uncountable ordinal number, ω1 or Ω
*As part of logo or trademark:
** The logo of Omega Watches
Omega SA is a Swiss luxury watchmaker based in Biel/Bienne, Switzerland. Founded by Louis Brandt in La Chaux-de-Fonds in 1848, the company formerly operated as ''La Generale Watch Co.'' until incorporating the name ''Omega'' in 1903, becoming ' ...
SA.
** The logo of Omegaklinikken
** Part of the original Pioneer logo.
** 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
A war god in mythology associated with war, combat, or bloodshed. They occur commonly in both monotheistic and polytheistic religions.
Unlike most gods and goddesses in polytheistic religions, monotheistic deities have traditionally been p ...
'' video game series based on Greek mythology. In God of War (2018), it is revealed it stands as the symbol of war in Greece.
** The logo of E-123 Omega
The '' Sonic the Hedgehog'' video game franchise began in 1991 with the game '' Sonic the Hedgehog'' for the Sega Genesis, which pitted a blue anthropomorphic hedgehog named Sonic against a rotund male human villain named Doctor Eggman (or Doc ...
, a '' Sonic the Hedgehog'' character.
** The logo of the Heroes of Olympus
''The Heroes of Olympus'' is a pentalogy of fantasy- adventure novels written by American author Rick Riordan. The novels detail a conflict between Greek demigods, Roman demigods, and Gaia (Roman name Terra). In the fourth book of the series, ...
series, based on Greek mythology.
** the logo of the Ultramarines in '' Warhammer 40,000''
** The logo of Primal Groudon, the version mascot of '' Pokémon Omega Ruby''.
** The logo of Darkseid in DC comics
** One of the logos of professional wrestler Kenny Omega
** The logo for Meow Wolf
Meow Wolf is an American arts and entertainment company that creates large-scale interactive and immersive art installations. Founded in 2008, its flagship attraction, ''House of Eternal Return'' in Santa Fe, New Mexico, is a facility, which ...
's Omega Mart
Omega Mart is an interactive art installation created by American arts company Meow Wolf and located in the Area15 complex in Las Vegas. Those entering the installation explore a supermarket, from which they can access various other areas and ...
in Area15, Las Vegas, Nevada.
** The logo for AMPLY Power’s Omega™ Charge Management System.
** The logo of Lalaji Memorial Omega International School
Lalaji Memorial Omega International School is a co-educational International day and boarding school situated on in Chennai, India, with more than 5000 students. The foundation stone of the school building was laid in 2005 by its promoter, Sri ...
*Other:
** The symbol of the resistance movement against the Vietnam-era draft in the United States
** Year or date of death
** In eschatology
Eschatology (; ) concerns expectations of the end of the present age, human history, or of the world itself. The end of the world or end times is predicted by several world religions (both Abrahamic and non-Abrahamic), which teach that nega ...
, the symbol for the end of everything
**In molecular biology
Molecular biology is the branch of biology that seeks to understand the molecular basis of biological activity in and between cells, including biomolecular synthesis, modification, mechanisms, and interactions. The study of chemical and phys ...
, the symbol is used as shorthand to signify a genetic construct introduced by a two-point crossover
** Omega Particle in the Star Trek universe
''Star Trek'' is an American science fiction media franchise created by Gene Roddenberry, which began with the eponymous 1960s television series and quickly became a worldwide pop-culture phenomenon. The franchise has expanded into vario ...
** The final form of NetNavi bosses in some of the ''Mega Man Battle Network
is a tactical role-playing video game series created by Masahiro Yasuma and developed and published by Capcom as a spin-off of the ''Mega Man'' series; it premiered in 2001 on the Game Boy Advance and takes place in an alternate continuity wh ...
'' games
** The personal symbol for Death, as worn by Death in the Discworld series by Terry Pratchett
** A secret boss in the ''Final Fantasy
is a Japanese science fantasy anthology media franchise created by Hironobu Sakaguchi and developed and owned by Square Enix (formerly Square). The franchise centers on a series of fantasy and science fantasy role-playing video games. The ...
'' series called Omega ( Ω ) Weapon.
** A character from the series '' Doctor Who'' called Omega, believed to be one of the creators of the Time Lords of Gallifrey.
** The symbol for the highest power level of a PSI attack in the ''MOTHER
]
A mother is the female parent of a child. A woman may be considered a mother by virtue of having given birth, by raising a child who may or may not be her biological offspring, or by supplying her ovum for fertilisation in the case of ...
/ EarthBound'' games
The symbol ω (lower case letter)
The minuscule letter ω is used as a symbol:
* Biology, biochemistry and chemistry:
** In biochemistry
Biochemistry or biological chemistry is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology and ...
, 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 biology, for fitness
** In chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, proper ...
, for denoting the carbon atom furthest from the carboxyl group of a fatty acid
In chemistry, particularly in biochemistry, a fatty acid is a carboxylic acid with an aliphatic chain, which is either saturated or unsaturated. Most naturally occurring fatty acids have an unbranched chain of an even number of carbon atoms, f ...
** In genomics, as a measure of molecular evolution
Molecular evolution is the process of change in the sequence composition of cellular molecules such as DNA, RNA, and proteins across generations. The field of molecular evolution uses principles of evolutionary biology and population genet ...
in protein-coding genes (also denoted as dN/dS or Ka/Ks ratio)
* Physics
** Angular velocity or angular frequency
In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit ti ...
** In computational fluid dynamics
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate ...
, the specific turbulence dissipation rate
** In meteorology
Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did no ...
, the change of pressure with respect to time of a parcel of air
** In circuit analysis
A network, in the context of electrical engineering and electronics, is a collection of interconnected components. Network analysis is the process of finding the voltages across, and the currents through, all network components. There are many ...
and signal processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing '' signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, ...
to represent natural frequency, related to frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
''f'' by ω = 2π''f''
** In astronomy
Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...
, as a ranking of a star's brightness within a constellation
** In orbital mechanics, as designation of the argument of periapsis of an orbit
** In particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
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
** In APL, to represent the right parameter to a function
*Mathematics:
** The first and smallest transfinite ordinal number, often identified with the set of natural numbers including 0 (sometimes written )
** In set theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concern ...
, ω1 is the first uncountable ordinal number (also sometimes written as Ω)
** A primitive root of unity
In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that yields 1 when raised to some positive integer power . Roots of unity are used in many branches of mathematics, and are especially important i ...
, like the complex cube roots of 1
** The Wright Omega function
** A generic differential form
In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many application ...
** 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
** Clique number
In the mathematical area of graph theory, a clique ( or ) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent. That is, a clique of a graph G is an induced subgraph of G that is compl ...
in Graph theory
In mathematics, graph theory is the study of '' graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...
* Other:
** Used in place of ん in Japanese typing shorthand.
** In linguistics
Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure. Ling ...
, the phonological word
The phonological word or prosodic word (also called pword, PrWd; symbolised as ω) is a constituent in the phonological hierarchy higher than the syllable and the foot but lower than intonational phrase and the phonological phrase. It is largely ...
** In textual criticism, the archetype
The concept of an archetype (; ) appears in areas relating to behavior, historical psychology, and literary analysis.
An archetype can be any of the following:
# a statement, pattern of behavior, prototype, "first" form, or a main model that ...
of a manuscript tradition
** In sociology
Sociology is a social science that focuses on society, human social behavior, patterns of social relationships, social interaction, and aspects of culture associated with everyday life. It uses various methods of empirical investigation an ...
, used to refer to the lowest ranking member of a group
** In shift_JIS art
Shift_JIS art is artwork created from characters in the Shift JIS character set, a superset of the ASCII encoding standard intended for Japanese usage. Shift_JIS art has become popular on web-based bulletin boards, notably 2channel, and has e ...
, used to represent the cat's mouth. (e.g. (´・ω・`) ショボーン)
** In actuarial sciences, used to represent the maximum life span that characterizes a mortality table
In actuarial science and demography, a life table (also called a mortality table or actuarial table) is a table which shows, for each age, what the probability is that a person of that age will die before their next birthday ("probability of de ...
Character encodings
Greek omega/Coptic oou
[Unicode Code Charts]
Greek and Coptic (Range: 0370-03FF)
/ref>
Cyrillic omega
Latin
Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...
/IPA
IPA commonly refers to:
* India pale ale, a style of beer
* International Phonetic Alphabet, a system of phonetic notation
* Isopropyl alcohol, a chemical compound
IPA may also refer to:
Organizations International
* Insolvency Practitioners A ...
omega
Technical omega symbols
Mathematical omega
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 the style of the text.
Notes
{{Wiktionary, Ω, ω
Greek letters
Vowel letters