Omega

Encyclopedia

**Omega**is the 24th and last letter of the Greek alphabet

Greek alphabet

The Greek alphabet is the script that has been used to write the Greek language since at least 730 BC . The alphabet in its classical and modern form consists of 24 letters ordered in sequence from alpha to omega...

. In the Greek numeric system

Greek numerals

Greek numerals are a system of representing numbers using letters of the Greek alphabet. They are also known by the names Ionian numerals, Milesian numerals , Alexandrian numerals, or alphabetic numerals...

, it has a value of 800. The word literally means "great O" (

*ō mega*, mega meaning 'great'), as opposed to omicron

Omicron

Omicron is the 15th letter of the Greek alphabet. In the system of Greek numerals it has a value of 70. It is rarely used in mathematics because it is indistinguishable from the Latin letter O and easily confused with the digit 0...

, which means "little O" (

*o mikron*, micron meaning "little"). This name is Byzantine

Medieval Greek

Medieval Greek, also known as Byzantine Greek, is the stage of the Greek language between the beginning of the Middle Ages around 600 and the Ottoman conquest of the city of Constantinople in 1453. The latter date marked the end of the Middle Ages in Southeast Europe...

; in Classical Greek

Ancient Greek

Ancient Greek is the stage of the Greek language in the periods spanning the times c. 9th–6th centuries BC, , c. 5th–4th centuries BC , and the c. 3rd century BC – 6th century AD of ancient Greece and the ancient world; being predated in the 2nd millennium BC by Mycenaean Greek...

, the letter was called

*ō*, whereas the omicron was called

*ou*. The form of the uppercase letter derives from that of an omicron (Ο) broken up at the side , with the edges subsequently turned outwards . The modern lowercase shape goes back to the uncial

Uncial

Uncial is a majuscule script commonly used from the 3rd to 8th centuries AD by Latin and Greek scribes. Uncial letters are written in either Greek, Latin, or Gothic.-Development:...

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 upwards.

Phonetically, the Ancient Greek Ω is a long

Vowel length

In linguistics, vowel length is the perceived duration of a vowel sound. Often the chroneme, or the "longness", acts like a consonant, and may etymologically be one, such as in Australian English. While not distinctive in most dialects of English, vowel length is an important phonemic factor in...

open-mid

*o*[ɔː], equal to the vowel of British English

*raw*. In Modern Greek

Modern Greek

Modern Greek refers to the varieties of the Greek language spoken in the modern era. The beginning of the "modern" period of the language is often symbolically assigned to the fall of the Byzantine Empire in 1453, even though that date marks no clear linguistic boundary and many characteristic...

Ω represents the same sound as omicron. The letter omega is transcribed

Transcription (linguistics)

Transcription in the linguistic sense is the systematic representation of language in written form. The source can either be utterances or preexisting text in another writing system, although some linguists only consider the former as transcription.Transcription should not be confused with...

*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

Set theory

Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...

, in contrast to alpha

Alpha (letter)

Alpha is the first letter of the Greek alphabet. In the system of Greek numerals it has a value of 1. It was derived from the Phoenician letter Aleph...

, the first letter of the Greek alphabet. In the New Testament book of Revelation, God is declared to be the "alpha and omega

Alpha and Omega

The term Alpha and Omega comes from the phrase "I am the alpha and the omega" , an appellation of Jesus in the Book of Revelation ....

, the beginning and the end, the first and the last".

Omega was also adopted into the early Cyrillic alphabet

Early Cyrillic alphabet

The Early Cyrillic alphabet is a writing system developed in the First Bulgarian Empire in the 9th or 10th century to write the Old Church Slavonic liturgical language...

. See Cyrillic omega

Omega (Cyrillic)

Omega is a letter used in the early Cyrillic alphabet. Its name and form are derived from the Greek letter Omega .Unlike Greek, the Slavic languages had only a single /o/ sound, so Omega was little used compared to the letter On , descended from the Greek letter Omicron...

. A Raetic variant is conjectured to be at the origin or parallel evolution of the Elder Futhark

Elder Futhark

The Elder Futhark is the oldest form of the runic alphabet, used by Germanic tribes for Northwest Germanic and Migration period Germanic dialects of the 2nd to 8th centuries for inscriptions on artifacts such as jewellery, amulets, tools, weapons and runestones...

ᛟ.

## The symbol Ω (majuscule letter)

The majuscule letter Ω is used as a symbol:- In chemistryChemistryChemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

:- For Oxygen-18Oxygen-18Oxygen-18 is a natural, stable isotope of oxygen and one of the environmental isotopes.18O is an important precursor for the production of fluorodeoxyglucose used in positron emission tomography...

a natural, stable isotope of oxygen

- For Oxygen-18
- In physicsPhysicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

:- For ohmOhmThe ohm is the SI unit of electrical resistance, named after German physicist Georg Simon Ohm.- Definition :The ohm is defined as a resistance between two points of a conductor when a constant potential difference of 1 volt, applied to these points, produces in the conductor a current of 1 ampere,...

– SISiSi, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

unit of electrical resistance; formerly also used upside down to represent mho, the old name for the inverse of an ohm (now siemensSiemens (unit)The siemens is the SI derived unit of electric conductance and electric admittance. Conductance and admittance are the reciprocals of resistance and impedance respectively, hence one siemens is equal to the reciprocal of one ohm, and is sometimes referred to as the mho. In English, the term...

with symbol S) used for electrical conductance. UnicodeUnicodeUnicode is a computing industry standard for the consistent encoding, representation and handling of text expressed in most of the world's writing systems...

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. - In statistical mechanicsStatistical mechanicsStatistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...

Ω refers to the multiplicity (number of microstates) in a system. - The solid angleSolid angleThe solid angle, Ω, is the two-dimensional angle in three-dimensional space that an object subtends at a point. It is a measure of how large that object appears to an observer looking from that point...

or the rate of precession in a gyroscope. - In particle physicsParticle physicsParticle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...

to represent the Omega baryons. - In astronomyAstronomyAstronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

(cosmologyPhysical cosmologyPhysical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion...

) Ω refers to the density of the universe, also called the density parameter. - In astronomy (orbital mechanics), Ω refers to the longitude of the ascending nodeLongitude of the ascending nodeThe longitude of the ascending node is one of the orbital elements used to specify the orbit of an object in space. It is the angle from a reference direction, called the origin of longitude, to the direction of the ascending node, measured in a reference plane...

of an orbit

- For ohm
- In mathematicsMathematicsMathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

/ computer scienceComputer scienceComputer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...

:- in notation related to Big O notationBig O notationIn mathematics, big O notation is used to describe the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann-Landau notation, or...

to describe the asymptotic behavior of functionFunction (mathematics)In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...

s. - Chaitin's constantChaitin's constantIn the computer science subfield of algorithmic information theory, a Chaitin constant or halting probability is a real number that informally represents the probability that a randomly constructed program will halt...

.

- in notation related to Big O notation
- In mathematics
- In complex analysisComplex analysisComplex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...

, 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 theorySet theorySet theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...

, the first uncountable ordinal numberFirst uncountable ordinalIn mathematics, the first uncountable ordinal, traditionally denoted by ω1 or sometimes by Ω, is the smallest ordinal number that, considered as a set, is uncountable. It is the supremum of all countable ordinals...

(more commonly written as ω_{1}) - In topos theory, the (codomain of the) subobject classifierSubobject classifierIn category theory, a subobject classifier is a special object Ω of a category; intuitively, the subobjects of an object X correspond to the morphisms from X to Ω. As the name suggests, what a subobject classifier does is to identify/classify subobjects of a given object according to which elements...

of an elementary topos. - In combinatory logicCombinatory logicCombinatory logic is a notation introduced by Moses Schönfinkel and Haskell Curry to eliminate the need for variables in mathematical logic. It has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming...

, the looping combinator,*(λ x. x x) (λ x. x x)* - In group theoryGroup theoryIn mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...

, the omega and agemo subgroupOmega and agemo subgroupIn 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 structure was sufficiently similar to that of finite abelian...

s of a*p*-group, Ω(*G*) and ℧(*G*) - In statisticsStatisticsStatistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

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

- In complex analysis
- As part of logo or trademark:
- The logo of Omega WatchesOmega WatchesOmega SA is a Swiss luxury watchmaker based in Biel/Bienne, Switzerland. Omega is one of the most well-known and recognized watches in the world. Omega watch was the choice of NASA and the first watch on the Moon in 1969. Omega was the official timekeeping device of the Olympic Games. James Bond...

SA. - 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 Omega Watches

- In fictional worlds:
- In the fictional world of Star TrekStar TrekStar Trek is an American science fiction entertainment franchise created by Gene Roddenberry. The core of Star Trek is its six television series: The Original Series, The Animated Series, The Next Generation, Deep Space Nine, Voyager, and Enterprise...

, the Omega symbol is used in conjunction with the Omega Directive. - As the logo of the popular PlayStationPlayStationThe is a 32-bit fifth-generation video game console first released by Sony Computer Entertainment in Japan on December 3, .The PlayStation was the first of the PlayStation series of consoles and handheld game devices. The PlayStation 2 was the console's successor in 2000...

franchise*God of War*, a series of games based around Greek mythology.God of War (series)God of War is a series of action-adventure video games based on Greek mythology.The main trilogy—God of War I, II, & III—in the series were developed by Sony Computer Entertainment's Santa Monica division , with Ready at Dawn Studios developing the PSP and Javaground the mobile phone installment... - In the fictional universe Warhammer 40,000Warhammer 40,000Warhammer 40,000 is a tabletop miniature wargame produced by Games Workshop, set in a dystopian science fantasy universe. Warhammer 40,000 was created by Rick Priestley in 1987 as the futuristic companion to Warhammer Fantasy Battle, sharing many game mechanics...

, the symbol for the Sons of Orar Chapter and, if turned upside down, the symbol for the Ultramarine Chapter of the Space MarinesSpace Marines (Warhammer 40,000)In the fictional universe of Warhammer 40,000 setting created by Games Workshop, Space Marines are genetically modified "super human" soldiers created by the Emperor to conquer the galaxy and defend mankind. According to Games Workshop, there are over a thousand recorded chapters of Space Marines,...

. - In the
*X-Men*filmsX-Men (film series)The X-Men film series consists of superhero films based on the Marvel Comics superhero team of the same name. The films star an ensemble cast, focusing on Hugh Jackman as Wolverine, who is drawn into the conflict between Professor Xavier and Magneto , who have opposing views on humanity's...

the symbol is used in tattoos by mutantsMutant (Marvel Comics)In comic books published by Marvel Comics, a mutant is an organism who possesses a genetic trait called an X-gene that allows the mutant to naturally develop superhuman powers and abilities...

(particularly those who join the Brotherhood of MutantsBrotherhood of MutantsThe Brotherhood of Mutants, originally known as the Brotherhood of Evil Mutants, is a fictional Marvel Comics supervillain team devoted to mutant superiority over normal humans. They are among the chief adversaries of the X-Men...

) to publicly announce their mutant status. - In the DC UniverseDC UniverseThe DC Universe is the shared universe where most of the comic stories published by DC Comics take place. The fictional characters Superman, Batman and Wonder Woman are well-known superheroes from this universe. Note that in context, "DC Universe" is usually used to refer to the main DC continuity...

, the Omega symbol is associated mostly with DarkseidDarkseidDarkseid is a fictional character that appears in comic books published by DC Comics. The character first appeared in Superman's Pal Jimmy Olsen #134 and was created by writer-artist Jack Kirby....

. - In the BBCBBCThe British Broadcasting Corporation is a British public service broadcaster. Its headquarters is at Broadcasting House in the City of Westminster, London. It is the largest broadcaster in the world, with about 23,000 staff...

sci-fi television series*Doctor Who*, the symbol is used by and to represent the character Omega.Doctor WhoDoctor Who is a British science fiction television programme produced by the BBC. The programme depicts the adventures of a time-travelling humanoid alien known as the Doctor who explores the universe in a sentient time machine called the TARDIS that flies through time and space, whose exterior...

- In the fictional world of Star Trek

- Other
- The symbol of the resistance movement against the Vietnam-era draft
- Year or date of death
- Used to refer to the lowest-ranked wolf in a pack

## The symbol ω (minuscule letter)

The minuscule letter ω is used as a symbol:- Biochemistry and chemistry:
- Denotes the carbon atom furthest from the carboxyl group of a fatty acidFatty acidIn chemistry, especially biochemistry, a fatty acid is a carboxylic acid with a long unbranched aliphatic tail , which is either saturated or unsaturated. Most naturally occurring fatty acids have a chain of an even number of carbon atoms, from 4 to 28. Fatty acids are usually derived from...

. - In biochemistryBiochemistryBiochemistry, sometimes called biological chemistry, is the study of chemical processes in living organisms, including, but not limited to, living matter. Biochemistry governs all living organisms and living processes...

, for one of the RNARNARibonucleic acid , or RNA, is one of the three major macromolecules that are essential for all known forms of life....

PolymerasePolymeraseA polymerase is an enzyme whose central function is associated with polymers of nucleic acids such as RNA and DNA.The primary function of a polymerase is the polymerization of new DNA or RNA against an existing DNA or RNA template in the processes of replication and transcription...

subunits. - In biochemistry, for the dihedral angle associated with the peptide group, involving the backbone atoms Cα-C'-N-Cα
- In genomicsGenomicsGenomics is a discipline in genetics concerning the study of the genomes of organisms. The field includes intensive efforts to determine the entire DNA sequence of organisms and fine-scale genetic mapping efforts. The field also includes studies of intragenomic phenomena such as heterosis,...

, as a measure of evolutionEvolutionEvolution is any change across successive generations in the heritable characteristics of biological populations. Evolutionary processes give rise to diversity at every level of biological organisation, including species, individual organisms and molecules such as DNA and proteins.Life on Earth...

at the protein level (also denoted as d_{N}/d_{S}or K_{a}/K_{s}ratioKa/Ks ratioIn genetics, the Ka/Ks ratio , is the ratio of the number of non-synonymous substitutions per non-synonymous site to the number of synonymous substitutions per synonymous site , which can be used as an indicator of selective pressure acting on a protein-coding gene...

).

- Denotes the carbon atom furthest from the carboxyl group of a fatty acid
- Physics:
- angular velocityAngular velocityIn physics, the angular velocity is a vector quantity which specifies the angular speed of an object and the axis about which the object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per...

or angular frequencyAngular frequencyIn physics, angular frequency ω is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity... - Computational fluid dynamicsComputational fluid dynamicsComputational fluid dynamics, usually abbreviated as CFD, is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the calculations required to simulate the interaction of liquids and gases with...

: the specific turbulence dissipation rate - In circuit analysis and signal processingSignal processingSignal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...

to represent natural frequency, related to frequencyFrequencyFrequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

*f*by ω = 2π*f* - In astronomyAstronomyAstronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

, as a ranking of a star's brightness - In astronomy (orbital mechanics), as designation of the argument of periapsisArgument of periapsisThe argument of periapsis , symbolized as ω, is one of the orbital elements of an orbiting body...

of an orbit - In particle physicsParticle physicsParticle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...

to represent the omega mesonMesonIn particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...

- angular velocity
- Computer science:
- In notation related to Big O notationBig O notationIn mathematics, big O notation is used to describe the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann-Landau notation, or...

, the asymptotically dominant nature of functionFunction (mathematics)In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...

s - In relational databaseRelational databaseA relational database is a database that conforms to relational model theory. The software used in a relational database is called a relational database management system . Colloquial use of the term "relational database" may refer to the RDBMS software, or the relational database itself...

theory to represent NULLNull (SQL)Null is a special marker used in Structured Query Language to indicate that a data value does not exist in the database. Introduced by the creator of the relational database model, E. F. Codd, SQL Null serves to fulfill the requirement that all true relational database management systems support...

, a missing or inapplicable value.

- In notation related to Big O notation
- Mathematics:
- The first transfiniteTransfinite numberTransfinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite. The term transfinite was coined by Georg Cantor, who wished to avoid some of the implications of the word infinite in connection with these...

ordinal numberOrdinal numberIn set theory, an ordinal number, or just ordinal, is the order type of a well-ordered set. They are usually identified with hereditarily transitive sets. Ordinals are an extension of the natural numbers different from integers and from cardinals...

, often identified with the set of natural numbers including 0 (sometimes written ) - The complex cube roots of 1
- The Wright Omega functionWright Omega functionIn mathematics, the Wright omega function, denoted ω, is defined in terms of the Lambert W function as:-Uses:One of the main applications of this function is in the resolution of the equation z = ln, as the only solution is given by z = e−ω.y = ω is the unique solution,...
- A generic differential formDifferential formIn the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates. Differential forms provide a better definition for integrands in calculus...
- In number theoryNumber theoryNumber theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...

, an arithmetic functionArithmetic functionIn number theory, an arithmetic function is a real or complex valued function ƒ defined on the set of natural numbers In number theory, an arithmetic (or arithmetical) function is a real or complex valued function ƒ(n) defined on the set of natural numbers In number theory, an arithmetic (or... - In combinatory logicCombinatory logicCombinatory logic is a notation introduced by Moses Schönfinkel and Haskell Curry to eliminate the need for variables in mathematical logic. It has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming...

, the self-application combinator,*(λ x. x x)* - In mathematical/options finance, the elasticity of financial options
- In analytical investment management, the tracking errorTracking errorIn finance, tracking error is a measure of how closely a portfolio follows the index to which it is benchmarked. The most common measure is the root-mean-square of the difference between the portfolio and index returns....

of an investment manager

- The first transfinite
- Other:
- Used in place of ん in Japanese typing shorthand.
- In linguisticsLinguisticsLinguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....

, the phonological wordPhonological wordThe phonological word or prosodic word is a constituent in the phonological hierarchy higher than the syllable and the foot but lower than intonational phrase and the phonological phrase... - In textual criticismTextual criticismTextual criticism is a branch of literary criticism that is concerned with the identification and removal of transcription errors in the texts of manuscripts...

, the archetypeArchetypeAn archetype is a universally understood symbol or term or pattern of behavior, a prototype upon which others are copied, patterned, or emulated...

of a manuscript tradition - In sociologySociologySociology is the study of society. It is a social science—a term with which it is sometimes synonymous—which uses various methods of empirical investigation and critical analysis to develop a body of knowledge about human social activity...

, used to refer to the lowest ranking member of a group