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Bet Here Νθ τθ Ωμεγα

Nu (/ˈnjuː/; uppercase Ν, lowercase ν; Greek: vι ni [ni]) is the thirteenth letter of the Greek alphabet, representing the voiced alveolar nasal IPA: [n]. In the system of Greek numerals it has a value of 50. It is derived from the Phoenician nun . Its Latin equivalent is N, though the lowercase ( $\nu$ ) resembles the Roman lowercase v.

The name of the letter is written νῦ in Ancient Greek and traditional Modern Greek polytonic orthography, while in Modern Greek it is written νι [ni].

Letters that arose from nu include Roman N and Cyrillic script En.

Symbology

Bust of Nikos Kazantzakis with the traditional Greek nu

The lower-case letter $ν$ is used as a symbol in many academic fields. Uppercase nu is not used, because it appears identical to Latin N.

Mathematics:
- Degrees of freedom in statistics.
- The greatest fixed point of a function, as commonly used in the μ-calculus.
- Free names of a process, as used in the π-calculus.
- One of the Greeks in mathematical finance, known as "vega".
- The reciprocal of 1 plus the interest rate in finance.
- The $p$ -adic valuation or $p$ -adic order of a number.
Physics:
- Kinematic viscosity in fluid mechanics.
- The frequency^[1] of a wave in physics and other fields; sometimes also spatial frequency; wavenumber
- The specific volume in thermodynamics.
- Poisson's ratio, the ratio of strains perpendicular with and parallel with an applied force.
- Any of three kinds of neutrino in particle physics.
- The number of neutrons released per fission of an atom in nuclear physics.
- Molecular vibrational mode, $ν x$ where $x$ is the number of the vibration (a label).
- The true anomaly, an angular parameter that defines the position of a body moving along an orbit (see orbital elements).
Biology:
- A DNA polymerase found in higher eukaryotes and implicated in translesion synthesis.
Chemistry:
- The stoichiometric coefficient.
Psychology:

The maximum conditioning possible for an unconditioned stimulus in the Rescorla-Wagner model.

Xi (UK: /zaɪ/, US: /ksaɪ/;^[1]^[2] uppercase Ξ, lowercase ξ; Greek: ξι) is the fourteenth letter of the Greek alphabet, representing the voiceless consonant cluster [ks]. Its name is pronounced [ksi] in Modern Greek. In the system of Greek numerals, it has a value of 60. Xi was derived from the Phoenician letter samekh .

Xi is distinct from the letter chi, which gave its form to the Latin letter X.

Greek

A joined variant of Ξ (New Athena Unicode font)

Both in classical Ancient Greek and in Modern Greek, the letter Ξ represents the consonant cluster /ks/. In some archaic local variants of the Greek alphabet, this letter was missing. Instead, especially in the dialects of most of the Greek mainland and Euboea, the cluster /ks/ was represented by Χ (which in classical Greek is chi, used for /kʰ/).

Because this variant of the Greek alphabet was used in Magna Graecia (the Greek colonies in Sicily and the southern part of the Italian peninsula), the Latin alphabet borrowed Χ rather than Ξ as the Latin letter that represented the /ks/ cluster that was also present in Latiν

Pure mathematics

Random variables
A parameter in a generalized Pareto distribution
The symmetric function equation of the Riemann zeta function in mathematics, also known as the Riemann Xi function
A universal set in set theory
A number used in the remainder term of Taylor's theorem that falls between the limits a and b
A number used in error approximations for formulas that are applications of Taylor's theorem, such as Newton–Cotes formulas

Physics and astronomy

In fluid dynamics, the Iribarren parameter.
The initial mass function in astronomy.
The correlation function in astronomy.
Spatial frequency;^[3] also sometimes temporal frequency.
A small displacement in MHD plasma stability theory
The x-coordinate of computational space as used in computational fluid dynamics
Potential difference in physics (in volts)
The radial integral in the spin-orbit matrix operator in atomic physics.
The Killing vector in general relativity.
Average logarithmic energy decrement per collision (neutron calculations in nuclear physics)
Pippard's cohesion length in superconductors
The diameter of a crystal nucleus in nucleation theory
Microturbulence velocity in a stellar atmosphere
The dimensionless longitudinal momentum loss of a beam particle after a two-body interaction in accelerator physics.
Dimensionless distance variable used in the Lane–Emden equation

Other uses

Propositional variables in some philosophical works, first found in Wittgenstein's Tractatus
Extent of reaction, a concept in physical chemistry^[4] used often in chemical engineering kinetics and thermochemistry
Unknown stereochemistry or stereocentre configuration in a planar ring system in organic chemistry,^[5] as well as uppercase Xi for unknown R/S/E/Z configuration in general^[6]
One of the two different polypeptide chains of the human embryonic hemoglobin types Hb-Portland (ξ₂γ₂) and Hb-Gower I (ξ₂ε₂)
A parameter denoted as warped time used to derive the equations for homogeneous azeotropic distillation
State Price Density in mathematical finance
The information vector in the Information Filter, GraphSLAM, and a number of other algorithms used for robot localization and robotic mapping.
Used in Support Vector machines in cases where the data is not linearly separable.
Used in Microelectronics to represent the distance from a p-n junction to a point in the depletion region where the electric field is strongest.

Omicron (US: /ˈoʊmɪkrɒn, ˈɒmɪkrɒn/, UK: / oʊˈmaɪkrɒn/;^[1] uppercase Ο, lowercase ο, Greek: όμικρον) is the fifteenth 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 IPA: [o] in contrast to omega which represented the open-mid back rounded vowel IPA: [ɔː] and the digraph ου which represented the long close-mid back rounded vowel IPA: [oː]. In modern Greek, both omicron and omega represent the mid back rounded vowel IPA: [o̞] or IPA: [ɔ̝]. Letters that arose from omicron include Roman O and Cyrillic O. The word literally means "little O" (o mikron) as opposed to "great O" (ō mega).^[2] In the system of Greek numerals, omicron has a value of 70.

Use

In addition to its use as an alphabetic letter, omicron is occasionally used in technical notation,^{[citation needed]} but its use is limited since both upper case and lower case (Ο ο) are indistinguishable from the Latin letter "o" (O o) and difficult to distinguish from the Arabic numeral "zero" (0).

Mathematics

The big-O symbol introduced by Paul Bachmann in 1894 and popularized by Edmund Landau in 1909, originally standing for "order of" ("Ordnung") and being thus a Latin letter, was apparently viewed by Donald Knuth in 1976^[3] as a capital Omicron, probably in reference to his definition of the symbol (capital) Omega. Neither Bachmann nor Landau ever call it "Omicron", and the word "Omicron" appears just once in Knuth's paper: in the title.

Greek numerals

There were several systems for writing numbers in Greek; the most common form used in late classical era used omicron (either upper or lower case) to represent the value 70.

More generally, the letter omicron is used to mark the fifteenth ordinal position in any Greek-alphabet marked list. So, for example, in Euclid's Elements, when various points in a geometric diagram are marked with letters, it is effectively the same as marking them with numbers, each letter representing the number of its place in the standard alphabet.^[a]^[b]

Astronomy

Omicron is used to designate the fifteenth star in a constellation group, its ordinal placement an irregular function of both magnitude and position.^[4]^[5] Such stars include Omicron Andromedae, Omicron Ceti, and Omicron Persei.

In Claudius Ptolemy's (c. 100–170) Almagest, tables of sexagesimal numbers $1 ... 59$ are represented in the conventional manner for Greek numbers:^[c] $'α 'β ... 'νη 'νθ$ . Since the letter omicron [which represents $70$ ( $'ο$ ) in the standard system] is not used in sexagesimal, it is re-purposed to represent an empty number cell. In some copies, zero cells were just left blank (nothing there, value is zero), but to avoid copying errors, positively marking a zero cell with omicron was preferred, for the same reason that blank cells in modern tables are sometimes filled-in with a long dash (—). Both an omicron and a dash imply that "this isn't a mistake, the cell is actually supposed to be empty". By coincidence, the ancient zero-value omicron ( $'ο$ ) resembles a modern Hindu-Arabic zero ( $0$ ).

Medicine

The World Health Organization (WHO) uses the Greek alphabet to describe variants of concern of SARS‑CoV‑2, the virus which causes COVID-19.^[6] On November 26, 2021, Omicron was assigned to the B.1.1.529 variant of concern.^[7]

History

Detail from a fifth century BCE inscription of Draco's law on homicide, showing the use of O rather than Ω in the phrase "ΠΡΟΤΟΣ ΑΧΣΟΝ" (

πρώτος ἄξων

, "first axon")

In the earliest Greek inscriptions, only five vowel letters A E I O Y were used. Vowel length was undifferentiated, with O representing both the short vowel /o/ and the long vowels /o:/ and /ɔː/.^[8]^(p 19) Later, in classical Attic Greek orthography, the three vowels were represented differently, with O representing short /o/, the new letter Ω representing long /ɔː/, and the so-called "spurious diphthong" OY representing long /o:/.^[8]^{(pp 56, 71)}

Although the Greeks took the character O from the Phoenician letter `ayin, they did not borrow its Phoenician name. Instead, the name of the letter O in classical Attic times was simply the long version of its characteric sound: $οὖ$ (pronounced /o:/) (that of Ω was likewise $ὦ$ ).^[9]^[d] By the second and third centuries CE, distinctions between long and short vowels began to disappear in pronunciation, leading to confusion between O and Ω in spelling. It was at this time that the new names of $ὂ μικρόν$ ("small O") for O $ὦ μέγα$ ("great O") for Ω were introduced.^[9]

Pi (/ˈpaɪ/; Ancient Greek /piː/ or /peî/, uppercase Π, lowercase π, cursive ϖ; Greek: πι [pi]) is the sixteenth letter of the Greek alphabet, meaning units united, and representing the voiceless bilabial plosive IPA: [p]. In the system of Greek numerals it has a value of 80. It was derived from the Phoenician letter Pe (). Letters that arose from pi include Latin P, Cyrillic Pe (П, п), Coptic pi (Ⲡ, ⲡ), and Gothic pairthra (𐍀).^[1]

Uppercase Pi

The uppercase letter Π is used as a symbol for:

In textual criticism, Codex Petropolitanus, a 9th-century uncial codex of the Gospels, now located in St. Petersburg, Russia.
In legal shorthand, it represents a plaintiff.
In Mathematical finance, it represents a portfolio.

In science and engineering:

The product operator in mathematics, indicated with capital pi notation $Π$ (in analogy to the use of the capital Sigma $Σ$ as summation symbol).
The osmotic pressure in chemistry.
The viscous stress tensor in continuum mechanics and fluid dynamics.

Lowercase Pi

The lowercase letter $π$ is used as a symbol for:

The mathematical real transcendental (and thus irrational) constant π ≈ 3.14159..., the ratio of a circle's circumference to its diameter in Euclidean geometry. The letter " $π$ " is the first letter of the Greek words περιφέρεια 'periphery' and περίμετρος 'perimeter', i.e. the circumference.
The prime-counting function in mathematics.
Homotopy groups in algebraic topology.
Dimensionless parameters constructed using the Buckingham π theorem of dimensional analysis.
The hadron called the pion (pi meson).
Often inflation rate in macroeconomics.
Sometimes profit in microeconomics.
A type of chemical bond in which the p orbitals overlap, called a pi bond.
The natural projection on the tangent bundle on a manifold.
The unary operation of projection in relational algebra.
Policy in reinforcement learning.

The earliest polyamory pride flag design, created by Jim Evans in 1995, in which the lowercase letter π stands for the first letter of polyamory.

Polyamory (in the earliest polyamory pride flag design, created by Jim Evans in 1995, pi stands for the first letter of polyamory).^[2]^[3]^[4]^[5]

History

This section needs expansion. You can help by adding to it. (March 2024)

An early form of pi was , appearing almost like a gamma with a hook.^[6]^[7]

Variant pi

Variant pi or "pomega" ( $\varpi \,\!$ or ϖ) is a glyph variant of lowercase pi sometimes used in technical contexts. It resembles a lowercase omega with a macron, though historically it is simply a cursive form of pi, with its legs bent inward to meet. It was also used in the minuscule script. It is a symbol for:

Angular frequency of a wave in fluid dynamics (angular frequency is usually represented by $\omega$ but this may be confused with vorticity in a fluid dynamics context).
Longitude of pericenter in celestial mechanics.^[8]
Comoving distance in cosmology.^[9]
Single-scattering albedo in radiative transfer.
Mean fitness of a population in biology.
Fundamental weights of a representation (probably to better distinguish from elements $w$ of the Weyl group, than the usual notation $\omega$ ).
The lemniscate constant.^[10]

Rho (/ˈroʊ/; uppercase Ρ, lowercase ρ or ϱ; Greek: ρο or ρω) is the seventeenth letter of the Greek alphabet. In the system of Greek numerals it has a value of 100. It is derived from Phoenician letter res

. Its uppercase form uses the same glyph, Ρ, as the distinct Latin letter P; the two letters have different Unicode encodings.

Uses

The Greek alphabet on a black figure vessel, with an R-shaped rho.

Greek

Rho is classed as a liquid consonant (together with Lambda and sometimes the nasals Mu and Nu), which has important implications for morphology. In both Ancient and Modern Greek, it represents an alveolar trill IPA: [r], alveolar tap IPA: [ɾ], or alveolar approximant IPA: [ɹ].

In polytonic orthography, a rho at the beginning of a word is written with a rough breathing, equivalent to h (ῥ rh), and a double rho within a word is written with a smooth breathing over the first rho and a rough breathing over the second (ῤῥ rrh). That apparently reflected an aspirated or voiceless pronunciation in Ancient Greek, which led to the various Greek-derived English words starting with rh or containing rrh.

The name of the letter is written in Greek as ῥῶ (polytonic) or ρω/ρο (monotonic).

Other alphabets

Letters that arose from rho include Roman R and Cyrillic Er (Р).

Mathematics and science

The characters ρ and ϱ are also conventionally used outside the Greek alphabetical context in science and mathematics.

In the physical sciences to represent:
- Densities: mass density, air density or charge density (ρ)
- Resistivity (ρ)
- Rho meson (ρ⁺, ρ⁻, ρ⁰)
- General quantum states
- Hammett Equation, ρ is used to represent the reaction constant, this is independent of the position and nature of the substituents of the benzene ring.
In mathematics to represent:
- A length coordinate in polar, cylindrical, spherical, and toroidal coordinate systems, and toroidal and poloidal coordinates of the Earth's magnetic field.
- The correlation coefficient of a population parameter
- The spectral radius of a matrix $A$ denoted as $\rho (A)$
- The plastic ratio
- The prime constant
- The sensitivity to interest rates of a pricing function
- The expected return of a given policy ( $\pi$ ) in reinforcement learning, denoted $\rho ^{\pi }$
- The rename operation in relational algebra
In economics to represent the discount rate of future pence cash flows
In molecular biology to represent the Rho protein responsible for termination of RNA synthesis. In such occasions, it is often represented as U+03F1 ϱ GREEK RHO SYMBOL, to avoid confusion with the Latin letter p
In molecular biology to represent the Rho family of GTPases, important for cytoskeletal dynamic regulation.
In ecology to represent the population damping ratio where ρ = λ1 / |λ2|.
In computer programming
- The lower-case rho "⍴" means reshape in the APL programming language, and by extension also queries shape
- The lower-case rho "ρ" is used for the unary rename operation in relational algebra
In statistics to represent Spearman's rank correlation coefficient, commonly known as Spearman's rho
In options theory to represent the rate of change of a portfolio with respect to interest rates

Chi Rho (☧)

The Chi Rho symbol representing Christ.

The letter rho overlaid with chi forms the Chi Rho symbol, used to represent Jesus Christ. It was first used by Emperor Constantine the Great. A can be seen on his standard known as the Labarum.

Rho with stroke (ϼ)

The rho with a stroke through its tail is used for abbreviations involving rho, most notably in γϼ for γράμμα as a unit of measurement.^[1]

Sigma (/ˈsɪɡmə/ SIG-mə;^[1] uppercase Σ, lowercase σ, lowercase in word-final position ς; Greek: σίγμα) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase Σ is used as an operator for summation. When used at the end of a letter-case word (one that does not use all caps), the final form (ς) is used. In Ὀδυσσεύς (Odysseus), for example, the two lowercase sigmas (σ) in the center of the name are distinct from the word-final sigma (ς) at the end. The Latin letter S derives from sigma while the Cyrillic letter Es derives from a lunate form of this letter.

History

The shape (Σς) and alphabetic position of sigma is derived from the Phoenician letter (shin).

Sigma's original name may have been san, but due to the complicated early history of the Greek epichoric alphabets, san came to be identified as a separate letter in the Greek alphabet, represented as Ϻ.^[2] Herodotus reports that "san" was the name given by the Dorians to the same letter called "sigma" by the Ionians.^[i]^[3]

According to one hypothesis,^[4] the name "sigma" may continue that of Phoenician samekh (), the letter continued through Greek xi, represented as Ξ. Alternatively, the name may have been a Greek innovation that simply meant 'hissing', from the root of σίζω (sízō, from Proto-Greek *sig-jō 'I hiss').^[2]

Lunate sigma

The Madaba Map, a sixth-century mosaic of Jerusalem (Η ΑΓΙΑ ΠΟΛΙϹ) uses the lunate sigma

A plaque reading "Metochion of Gethsemane" (Μετόχιον Γεθσημανῆς) in Jerusalem, with a lunate sigma both at the end and in the middle of the word

In handwritten Greek during the Hellenistic period (4th–3rd century BC), the epigraphic form of Σ was simplified into a C-like shape,^[5] which has also been found on coins from the 4th century BC onward.^[6] This became the universal standard form of sigma during late antiquity and the Middle Ages.

Today, it is known as lunate sigma (uppercase Ϲ, lowercase ϲ), because of its crescent-like shape, and is still widely used in decorative typefaces in Greece, especially in religious and church contexts, as well as in some modern print editions of classical Greek texts.

A dotted lunate sigma (sigma periestigmenon, Ͼ) was used by Aristarchus of Samothrace (220–143 BC) as an editorial sign indicating that the line marked as such is at an incorrect position. Similarly, a reversed sigma (antisigma, Ͻ), may mark a line that is out of place. A dotted antisigma (antisigma periestigmenon, Ͽ) may indicate a line after which rearrangements should be made, or to variant readings of uncertain priority.

In Greek inscriptions from the late first century BC onwards, Ͻ was an abbreviation indicating that a man's father's name is the same as his own name, thus Dionysodoros son of Dionysodoros would be written Διονυσόδωρος Ͻ (Dionysodoros Dionysodorou).^[7]^[8]

In Unicode, the above variations of lunate sigma are encoded as U+03F9 Ϲ GREEK CAPITAL LUNATE SIGMA SYMBOL; U+03FD Ͻ GREEK CAPITAL REVERSED LUNATE SIGMA SYMBOL, U+03FE Ͼ GREEK CAPITAL DOTTED LUNATE SIGMA SYMBOL, and U+03FF Ͽ GREEK CAPITAL REVERSED DOTTED LUNATE SIGMA SYMBOL.

Uses

Language and linguistics

In both Ancient and Modern Greek, the sigma represents the voiceless alveolar fricative [s]. In Modern Greek, this sound is voiced to the voiced alveolar fricative [z] when occurring before [m], [n], [v], [ð] or [ɣ].
The uppercase form of sigma (Σ) was re-borrowed into the Latin alphabet—more precisely, the International African Alphabet—to serve as the uppercase of modern esh (lowercase: ʃ).
In phonology, σ is used to represent syllables.
In linguistics, Σ represents the set of symbols that form an alphabet (see also computer science).
In historical linguistics, Σ is used to represent a Common Brittonic consonant with a sound between [s] and [h]; perhaps an aspirated [ʃʰ].^[9]

Science and mathematics

Mathematics

In general mathematics, lowercase σ is commonly used to represent unknown angles, as well as serving as a shorthand for "countably", whereas Σ is regularly used as the operator for summation, e.g.:

$\sum _{k=0}^{5}k=0+1+2+3+4+5=15$

In mathematical logic, $\Sigma _{n}^{0}$ is used to denote the set of formulae with bounded quantifiers beginning with existential quantifiers, alternating $n-1$ times between existential and universal quantifiers. This notation reflects an indirect analogy between the relationship of summation and products on one hand, and existential and universal quantifiers on the other. See the article on the arithmetic hierarchy.
In statistics, σ represents the standard deviation of population or probability distribution (where mu or μ is used for the mean).
In topology, σ-compact topological space is one that can be written as a countable union of compact subsets.
In mathematical analysis and in probability theory, there is a type of algebra of sets known as σ-algebra (aka σ-field). Sigma algebra also includes terms such as:
- σ(A), denoting the generated sigma-algebra of a set A
- Σ-finite measure (see measure theory)
In number theory, σ is included in various divisor functions, especially the sigma function or sum-of-divisors function.
In applied mathematics, σ(T) denotes the spectrum of a linear map T.
In complex analysis, σ is used in the Weierstrass sigma-function.
In probability theory and statistics, Σ denotes the covariance matrix of a set of random variables, sometimes in the form $\;|\!\!\!\Sigma$ to distinguish it from the summation operator.
Theoretical spectral analysis uses σ as standard deviation opposed to lowercase mu as the absolute mean value.

Biology, physiology, and medicine

In biology, the sigma receptor (σ–receptors) is a type of cell surface receptor.
In biochemistry, the σ factor (or specificity factor) is a protein found in RNA polymerase.
In bone physiology, the bone remodeling period—i.e., the life span of a basic multicellular unit—has historically been referred to as the sigma period
In early 20th-century physiology literature, σ had been used to represent milliseconds^[10]

Business, finance, and economics

In finance, σ is the symbol used to represent volatility of stocks, usually measured by the standard deviation of logarithmic returns.
In accounting, Σ indicates the balance of invoice classes and the overall amount of debts and demands.
In macroeconomics, σ is used in equations to represent the elasticity of substitution between two inputs.
In the machine industry, Six Sigma (6σ) is a quality model based on the standard deviation.

Chemistry

Sigma bonds (σ bonds) are the strongest type of covalent chemical bond.
In organic chemistry, σ symbolizes the sigma constant of Hammett equation.
In alchemy, Σ was sometimes used to represent sugar.

Engineering and computer science

In computer science, Σ represents the set of symbols that form an alphabet (see also linguistics)
Relational algebra uses the values $\sigma _{a\theta b}(R)$ and $\sigma _{a\theta v}(R)$ to denote selections, which are a type of unary operation.
In machine learning, σ is used in the formula that derives the Sigmoid function.
In radar jamming or electronic warfare, radar cross-sections (RCS) are commonly represented as σ when measuring the size of a target's image on radar.
In signal processing, σ denotes the damping ratio of a system parameter.
In theoretical computer science, Σ serves as the busy beaver function.
In civil engineering, σ refers to the normal stress applied on a material or structure.

Physics

In nuclear and particle physics, σ is used to denote cross sections in general (see also RCS), while Σ represents macroscopic cross sections [1/length].
The symbol is to denote the Stefan–Boltzmann constant.
In relation to fundamental properties of material, σ is often used to signify electrical conductivity.
In electrostatics, σ represents surface charge density.
In continuum mechanics, σ is used to signify stress.
In condensed matter physics, Σ denotes self-energy.
The symbol can be used to signify surface tension (alternatively, γ or T are also used instead).
In quantum mechanics, σ is used to indicate Pauli matrices.
In astronomy, σ represents velocity dispersion.
In astronomy, the prefix Σ is used to designate double stars of the Catalogus Novus Stellarum Duplicium by Friedrich Georg Wilhelm von Struve.
In particle physics, Σ represents a class of baryons.

Organizations

During the 1930s, an uppercase Σ was in use as the symbol of the Ação Integralista Brasileira, a fascist political party in Brazil.
Sigma Corporation uses the name of the letter but not the letter itself, but in many Internet forums, photographers refer to the company or its lenses using the letter.
Sigma Aldrich incorporate both the name and the character in their logo.

Tau (/ˈtɔː, ˈtɒ, ˈtaʊ/;^[1] uppercase Τ, lowercase τ or ${\boldsymbol {\tau }}$ ; Greek: ταυ [taf]) is the nineteenth letter of the Greek alphabet, representing the voiceless dental or alveolar plosive IPA: [t]. In the system of Greek numerals, it has a value of 300.

The name in English is pronounced /taʊ/ or /tɔː/,^[2] but in Greek it is [taf].^[3]^[4] This is because the pronunciation of the combination of Greek letters αυ can have the pronunciation of either [ai], [av] or [af], depending on what follows and if a diaeresis is present on the second vowel (see Greek orthography).

Tau was derived from the Phoenician letter taw (𐤕).^[5] Letters that arose from tau include Roman T and Cyrillic Te (Т, т).

The letter occupies the Unicode slots U+03C4 (lowercase) and U+03A4 (uppercase). In HTML, they can be produced with named entities (τ and Τ), decimal references (τ and Τ), or hexadecimal references (τ and Τ).

Modern usage

The lower-case letter τ is used as a symbol for:

Specific tax amount^[6]

Biology

The expressed period of the freerunning rhythm of an animal, i.e., the length of the daily cycle of an animal when kept in constant light or constant darkness
The dose interval in pharmacokinetics^[7]
The core variable in general tau theory
Tau in biochemistry, a protein associated with microtubules and implicated in neurodegenerative diseases such as Alzheimer's disease, some forms of frontotemporal lobar degeneration, and chronic traumatic encephalopathy^[8]^[9]

Mathematics

Divisor function in number theory, also denoted d or σ₀^[10]^{[note 1]}
Golden ratio (1.618...), although φ (phi) is more common^[11]^{[note 1]}
Kendall tau rank correlation coefficient in statistics^[12]
Stopping time in stochastic processes.^[13]^{[note 2]}
Tau, the ratio of the circumference to the radius of a circle, which is equal to 2 $π$ (6.28318...)^[14]^[15]
Tau functions, several
Torsion of a curve in differential geometry^[16]^{[note 1]}
Translation in Euclidean geometry (although the Latin letter T is used more often)
The Prouhet–Thue–Morse constant

Physics

Proper time in relativity
Shear stress in continuum mechanics
The lifetime of a spontaneous emission process
Tau, an elementary particle in particle physics
Tau in astronomy is a measure of optical depth, or how much sunlight cannot penetrate the atmosphere
In the physical sciences, tau is sometimes used as time variable, to avoid confusing t as temperature
Time constant (also relaxation time) of any system, such as an RC circuit
Torque, the rotational force in mechanics
The symbol for tortuosity in hydrogeology
In thermal physics, the symbol for the fundamental temperature $\tau =k_{B}T$

Symbolism

In ancient times, tau was used as a symbol for life or resurrection, whereas the eighth letter of the Greek alphabet, theta, was considered the symbol of death.^{[citation needed]}
In Biblical times, the taw was put on men to distinguish those who lamented sin, although newer versions of the Bible have replaced the ancient term taw with mark (Ezekiel 9:4) or signature (Job 31:35). Its original sound value is a voiceless alveolar plosive, IPA /t/^{[citation needed]}
The symbolism of the cross was connected not only to the letter chi but also to tau, the equivalent of the last letter in the Phoenician and Old Hebrew alphabets, and which was originally cruciform in shape; see Cross of Tau.^{[citation needed]}
An essay written around 160 AD, attributed to Lucian, a mock legal prosecution called The Consonants at Law - Sigma vs. Tau, in the Court of the Seven Vowels, contains a reference to the cross attribution. Sigma petitions the court to sentence Tau to death by crucifixion, saying:
Men weep, and bewail their lot, and curse Cadmus with many curses for introducing Tau into the family of letters; they say it was his body that tyrants took for a model, his shape that they imitated, when they set up structures on which men are crucified. Stauros (cross) the vile engine is called, and it derives its vile name from him. Now, with all these crimes upon him, does he not deserve death, nay, many deaths? For my part I know none bad enough but that supplied by his own shape — that shape which he gave to the gibbet named stauros after him by men
Tau is usually considered as the symbol of Franciscan orders due to St. Francis' love for it, symbol of the redemption and of the Cross. Almost all Franciscan churches have painted a tau with two crossing arms, both with stigmata, the one of Jesus and the other of Francis; members of the Secular Franciscan Order usually wear a wooden τ in a string with three knots around the neck
The title and symbol of "Tau" is used by neo-Gnostic bishops as it has some symbolism in many of the modern branches of Gnosticism.

Upsilon (US: /ˈʌpsɪˌlɒn, ˈ(j)uːp-, -lən/, UK: /(j)uːpˈsaɪlən, ʊp-, -lɒn/;^[1]^[2]^[3]^[4]^[5]^[6] uppercase Υ, lowercase υ; Greek: ύψιλον ýpsilon [ˈipsilon]) or ypsilon /ɪp-/^[1] is the twentieth letter of the Greek alphabet. In the system of Greek numerals, Υʹ has a value of 400. It is derived from the Phoenician waw .

The Greek alphabet on a black figure vessel, with a V-shaped upsilon

Etymology

The name of the letter was originally just "υ" (y; also called hy, hence "hyoid", meaning "shaped like the letter υ"), but the name changed to "υ ψιλόν" u psilon 'plain υ' to distinguish it from οι, which had come to have the same [y] pronunciation.^[7]

Pronunciation

In early Attic Greek (6th century BCE), it was pronounced [u] (a close back rounded vowel like the English "long o͞o").^[8]^[9] In Classical Greek, it was pronounced [y] (a close front rounded vowel), at least until 1030.^[10] In Modern Greek, it is pronounced [i]; in the digraphs αυ and ευ, as [f] or [v]; and in the digraph ου as [u]. In ancient Greek, it occurred in both long and short versions, but Modern Greek does not have a length distinction.

As an initial letter in Classical Greek, it always carried the rough breathing (equivalent to h) as reflected in the many Greek-derived English words, such as those that begin with hyper- and hypo-. This rough breathing was derived from an older pronunciation that used a sibilant instead; this sibilant was not lost in Latin, giving rise to such cognates as super- (for hyper-) and sub- (for hypo-).

Upsilon participated as the second element in falling diphthongs, which have subsequently developed in various ways.

Correspondence with Latin Y

Cyrillic У, Latin Y and Greek Υ and ϒ in FreeSerif – one of the few typefaces that distinguish between the Latin and the Greek form

The usage of Y in Latin dates back to the first century BC. It was used to transcribe loanwords from Greek, so it was not a native sound of Latin and was usually pronounced /u/ or /i/. The latter pronunciation was the most common in the Classical period and was used mostly by uneducated people. The Roman Emperor Claudius proposed introducing a new letter into the Latin alphabet to transcribe the so-called sonus medius (a short vowel before labial consonants), but in inscriptions, the new letter was sometimes used for Greek upsilon instead.

Four letters of the Latin alphabet arose from it: and U, Y and, much later, V and W. In the Cyrillic script, the letters U (У, у) and izhitsa (Ѵ, ѵ) arose from it.

In some languages, including German and Portuguese, the name upsilon (Ypsilon in German, ípsilon in Portuguese) is used to refer to the Latin letter Y as well as the Greek letter. In some other languages, the (Latin) Y is referred to as a "Greek I" (i griega in Spanish, i grec in French), also noting its Greek origin.

Usage

In particle physics the capital Greek letter ϒ denotes an Upsilon particle. Note that the symbol should always look like $\,\Upsilon$ in order to avoid confusion with a Latin Y denoting the hypercharge. This may be done either with a font such as FreeSerif or with the dedicated Unicode character U+03D2 ϒ.
Automobile manufacturer Lancia has a model called the Ypsilon. See Lancia Ypsilon.
In the International Phonetic Alphabet, the symbol ⟨ʋ⟩ is used to represent a labiodental approximant.
In astrophysics and physical cosmology, ϒ refers to the mass-to-light ratio.^[11]
In statistics, it is sometimes used instead of v or nu to indicate degrees of freedom^[12]
In the Farsi language, “one Upsilon” is used to describe a positive amount close to 0 (zero)

Similar appearance

A similar symbol (Unicode ♈ U+2648) is used for the astrological sign of Aries.

Symbolism

Geoffroy Tory Ypsilon

Upsilon is known as Pythagoras' letter, or the Samian letter, because Pythagoras used it as an emblem of the path of virtue or vice.^[13] As the Roman writer Persius wrote in Satire III:

and the letter which spreads out into Pythagorean branches has pointed out to you the steep path which rises on the right.^[14]

Lactantius, an early Christian author (ca. 240 – ca. 320), refers to this:

For they say that the course of human life resembles the letter Y, because every one of men, when he has reached the threshold of early youth, and has arrived at the place "where the way divides itself into two parts," is in doubt, and hesitates, and does not know to which side he should rather turn himself.^[15]

Phi (/faɪ/;^[1] uppercase Φ, lowercase φ or ϕ; Ancient Greek: ϕεῖ pheî [pʰéî̯]; Modern Greek: φι fi [fi]) is the twenty-first letter of the Greek alphabet.

In Archaic and Classical Greek (c. 9th to 4th century BC), it represented an aspirated voiceless bilabial plosive ([pʰ]), which was the origin of its usual romanization as ⟨ph⟩. During the later part of Classical Antiquity, in Koine Greek (c. 4th century BC to 4th century AD), its pronunciation shifted to a voiceless bilabial fricative ([ɸ]), and by the Byzantine Greek period (c. 4th century AD to 15th century AD) it developed its modern pronunciation as a voiceless labiodental fricative ([f]). The romanization of the Modern Greek phoneme is therefore usually ⟨f⟩.

It may be that phi originated as the letter qoppa (Ϙ, ϙ), and initially represented the sound /kʷʰ/ before shifting to Classical Greek [pʰ].^[2] In traditional Greek numerals, phi has a value of 500 (φʹ) or 500,000 (͵φ). The Cyrillic letter Ef (Ф, ф) descends from phi.

Like other Greek letters, lowercase phi (encoded as the Unicode character U+03C6 φ GREEK SMALL LETTER PHI) is used as a mathematical or scientific symbol. Some uses^{[example needed]} require the old-fashioned 'closed' glyph, which is separately encoded as the Unicode character U+03D5 ϕ GREEK PHI SYMBOL.

In lowercase

The lowercase letter φ (or its variant, ϕ or ɸ) is often used to represent the following:

The letter phi is commonly used in physics to represent wave functions in quantum mechanics, such as in the Schrödinger equation and bra–ket notation: $\langle \phi |\psi \rangle$ .
The golden ratio ${\tfrac {1+{\sqrt {5}}}{2}}\approx$ 1.618033988749894848204586834... in mathematics,^[3] art, and architecture. (Its reciprocal, 1/φ, is ${\tfrac {{\sqrt {5}}-1}{2}}$ and is equal to φ - 1.)
Euler's totient function φ(n) in number theory;^[4] also called Euler's phi function.
The cyclotomic polynomial functions Φ_n(x) of algebra.
The number of electrical phases in a power system in electrical engineering, for example 1ϕ for single phase, 3ϕ for three phase.
In algebra, group or ring homomorphisms
In probability theory, ${\textstyle \varphi (x)=(2\pi )^{-{\frac {1}{2}}}e^{-{\frac {x^{2}}{2}}}}$ is the probability density function of the standard normal distribution.
In probability theory, φ_X(t) = E[e^itX] is the characteristic function of a random variable X.
An angle, typically the second angle mentioned, after θ (theta). It can denote:
- The argument of a complex number.
- The phase of a wave in signal processing.
- In spherical coordinates, mathematicians usually refer to ϕ as the polar angle (from the z-axis). The convention in physics is to use ϕ as the azimuthal angle (from the x-axis).
- One of the dihedral angles in the backbones of proteins in a Ramachandran plot
- Internal or effective angle of friction.
- In cartography and navigation, ɸ denotes latitude; likewise, in geodesy it denotes geodetic latitude.
- In aircraft flight mechanics as the symbol for bank angle (sometimes represented with the letter theta, which is also used for pitch angle).
The work function of a surface, in solid-state physics.
A shorthand representation for an aromatic functional group in organic chemistry.
The fugacity coefficient in thermodynamics.
The ratio of free energy destabilizations of protein mutants in phi value analysis.
In combustion engineering, fuel–air equivalence ratio. The ratio between the actual fuel-air ratio to the stoichiometric fuel-air ratio.
In granulometry, sedimentology, and soil engineering, φ is a logarithmic unit of sediment grain size, defined such that a change of 1 φ in grain size corresponds to a factor of 2 in grain diameter.
A sentence in first-order logic.
The Veblen function in set theory.
Porosity in geology and hydrology.
Strength (or resistance) reduction factor in structural engineering, used to account for statistical variabilities in materials and construction methods.
The symbol for a voiceless bilabial fricative in the International Phonetic Alphabet (using the form ɸ).
In philosophy, φ is often used as shorthand for a generic act. (Also in uppercase.)^{[citation needed]}
In perceptual psychology, the phi phenomenon is the apparent motion caused by the successive viewing of stationary objects, such as the frames of a motion picture.
In linguistics, φ-features denote features such as case, number and gender in which adjectives and pronouns agree with nouns.
In lexical-functional grammar, the function that maps elements from the c-structure to the f-structure.
In ecology, site survival probability, or the probability that a species will continue to occupy a site if it was there the previous year.
The logo of La France Insoumise, a leftist French political party.
An abbreviation for the word bacteriophage
- Mϕ is used as an abbreviation for the word macrophage

In uppercase

The uppercase Φ is used as a symbol for:

The golden ratio conjugate −0.618... in mathematics.
The cumulative distribution function (cdf) of standard normal distribution in statistics.
The magnetic flux and electric flux in physics, with subscripts distinguishing the two.
Quantum yield, the number of times a specific event occurs per photon absorbed by a system.
In philosophy, Φ is often used as shorthand for a generic act. (Also in lowercase.)^{[citation needed]}
A common symbol for the parametrization of a surface in vector calculus.
In Lacanian algebra, Φ stands for the imaginary phallus and also represents phallic signification; −Φ stands in for castration.^[5]^{[dubious – discuss]}
The diameter symbol in engineering, ⌀, is often erroneously referred to as "phi", and the diameter symbol is sometimes erroneously typeset as Φ. This symbol is used to indicate the diameter of a circular section; for example, "⌀14" means the diameter of the circle is 14 units.
A clock signal in electronics is often called Phi or uses the symbol.^[6]
In emulsion and suspension science, Φ often denotes the volume fraction of the dispersed phase.^[7]
Archaically used in chemistry for phenyl group.

Chi (/ˈkaɪ, ˈxiː/ ^ⓘ;^[1]^[2] uppercase Χ, lowercase χ; Greek: χῖ) is the twenty-second letter of the Greek alphabet.

Greek

The Greek alphabet on a black figure vessel, with a cross-shaped chi

Pronunciation

Ancient Greek

Its value in Ancient Greek was an aspirated velar stop /kʰ/ (in the Western Greek alphabet: /ks/).

Koine Greek

In Koine Greek and later dialects it became a fricative ([x]/[ç]) along with Θ and Φ.

Modern Greek

In Modern Greek, it has two distinct pronunciations: In front of high or front vowels (/e/ or /i/) it is pronounced as a voiceless palatal fricative [ç], as in German ich or like some pronunciations of "h" in English words like hew and human. In front of low or back vowels (/a/, /o/ or /u/) and consonants, it is pronounced as a voiceless velar fricative ([x]), as in German ach or Spanish j. This distinction corresponds to the ich-Laut and ach-Laut of German.

Transliteration

Chi is romanized as ⟨ch⟩ in most systematic transliteration conventions, but sometimes ⟨kh⟩ is used.^[3] In addition, in Modern Greek, it is often also romanized as ⟨h⟩ or ⟨x⟩ in informal practice.

Greek numeral

In the system of Greek numerals, it has a value of 600.

Xi

In ancient times, some local forms of the Greek alphabet used the chi instead of xi to represent the /ks/ sound. This was borrowed into the early Latin language, which led to the use of the letter X for the same sound in Latin, and many modern languages that use the Latin alphabet.

Cyrillic

Chi was also included in the Cyrillic script as the letter Х, with the phonetic value /x/ or /h/.

International Phonetic Alphabet

In the International Phonetic Alphabet, ⟨ꭓ⟩ represents a voiceless uvular fricative.

Chiasmus

Chi is the basis for the name literary chiastic structure and the name of chiasmus.

Symbolism

In Plato's Timaeus, it is explained that the two bands that form the soul of the world cross each other like the letter Χ. Plato's analogy, along with several other examples of chi as a symbol occur in Thomas Browne's discourse The Garden of Cyrus (1658).

Chi or X is often used to abbreviate the name Christ, as in the holiday Christmas (Xmas). When fused within a single typeface with the Greek letter rho, it is called the Chi Rho and used to represent the person of Jesus Christ.

Math and science

In statistics, the term chi-squared or $\chi ^{2}$ has various uses, including the chi-squared distribution, the chi-squared test, and chi-squared target models.

In algebraic topology, Chi is used to represent the Euler characteristic of a surface.

In neuroanatomy, crossings of peripheral nerves (such as the optic chiasm) are named for the letter Chi because of its Χ-shape.^[5]

In chemistry, the mole fraction^[6]^[7] and electronegativity^[8] may be denoted by the lowercase $\chi$ .

In physics, $\chi$ denotes electric or magnetic susceptibility.

In rhetoric, both chiastic structure (a literary device) and the figure of speech Chiasmus derive from their names from the shape of the letter Chi.

In mechanical engineering, chi is used as a symbol for the reduction factor of relevant buckling loads in the EN 1993, a European Standard for the design of steel structures.

In graph theory, a lowercase chi is used to represent a graph's chromatic number.

In analytic number theory, chi is used for the Dirichlet character.

See also

Look up Χ or χ in Wiktionary, the free dictionary.

Chi (disambiguation)

Psi /ˈ(p)saɪ, ˈ(p)siː/ (P)SY, (P)SEE^[1] (uppercase Ψ, lowercase ψ or 𝛙; Greek: ψι psi [ˈpsi]) is the twenty-third and penultimate letter of the Greek alphabet and is associated with a numeric value of 700. In both Classical and Modern Greek, the letter indicates the combination /ps/ (as in English word "lapse").

For Greek loanwords in Latin and modern languages with Latin alphabets, psi is usually transliterated as "ps".

The letter's origin is uncertain. It may or may not derive from the Phoenician alphabet. It appears in the 7th century BC, expressing /ps/ in the Eastern alphabets, but /kʰ/ in the Western alphabets (the sound expressed by Χ in the Eastern alphabets). In writing, the early letter appears in an angular shape (). There were early graphical variants that omitted the stem ("chickenfoot-shaped psi" as: or ).^{[citation needed]}

The Western letter (expressing /kʰ/, later /x/) was adopted into the Old Italic alphabets, and its shape is also continued into the Algiz rune <ᛉ> of the Elder Futhark.

Psi, or its Arcadian variant or was adopted in the Latin alphabet in the form of "Antisigma" (Ↄ, ↃC, or 𐌟) during the reign of Emperor Claudius as one of the three Claudian letters.^[2] However, it was abandoned after his death.^{[citation needed]}

The classical Greek letter was adopted into the early Cyrillic alphabet as "Ѱ".

Use as a symbol

The letter psi is commonly used in physics to represent wave functions in quantum mechanics, such as in the Schrödinger equation and bra–ket notation: $\langle \phi |\psi \rangle$ . It is also used to represent the (generalized) positional states of a qubit in a quantum computer.

Psi is also used as the symbol for the polygamma function, defined by

\psi ^{(m)}(z)={\frac {d^{m}}{dz^{m}}}{\frac {\Gamma '(z)}{\Gamma (z)}}

where $\Gamma (z)$ is the gamma function.

The letters Ψ or ψ can also be a symbol for:

Psychology, psychiatry, and sometimes parapsychology (involving paranormal or relating with the supernatural subjects, especially research into extrasensory perception).
In mathematics, the reciprocal Fibonacci constant, the division polynomials, and the supergolden ratio.
Water potential in movement of water between plant cells.
In biochemistry, it denotes pseudouridine, an uncommon nucleoside.^[3]
Stream function in fluid mechanics defining the curve to which the flow velocity is always tangent.
One of the dihedral angles in the backbones of proteins.
The planet Neptune.
Indiana University (as a superimposed I and U).^[4]
A sai, the name of which is pronounced the same way in English.
Pharmacology, general pharmacy.
In virology the ψ site is a viral packaging signal.
The J/ψ meson, in particle physics.
In the computability theory, $\psi _{P}(x)\,\!$ represents the return value $Y\,\!$ of a program $P\,\!$ .
In circadian physiology, ψ represents the phase relationship between a zeitgeber and a biological rhythm.
In building, to represent an adjustment to a U-value, accounting for thermal bridge effects.
The ordinal collapsing function and notation developed by Wilfried Buchholz.^[5]
In Biblical studies, as an abbreviation for the book of Psalms.^[6]

Omega (US: /oʊˈmeɪɡə, -ˈmɛɡə, -ˈmiːɡə/, UK: /ˈoʊmɪɡə/;^[1] uppercase Ω, lowercase ω; Ancient Greek ὦ, later ὦ μέγα, Modern Greek ωμέγα) is the twenty-fourth and last letter in the Greek alphabet. In the Greek numeric system/isopsephy (gematria), it has a value of 800. The word literally means "great O" (o mega, mega meaning "great"), as opposed to omicron, which means "little O" (o mikron, micron meaning "little").^[2]

In phonetic terms, the Ancient Greek Ω represented a long open-mid back rounded vowel IPA: [ɔː], comparable to the "aw" of the English word raw in dialects without the cot–caught merger, in contrast to omicron which represented the close-mid back rounded vowel IPA: [o] , and the digraph ου which represented the long close-mid back rounded vowel IPA: [oː]. In Modern Greek, both omega and omicron represent the mid back rounded vowel IPA: [o̞] or IPA: [ɔ̝]. 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, in contrast to alpha, 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 open-mid back rounded vowel [ɔː]. It is a variant of omicron (Ο), broken up at the side (), with the edges subsequently turned outward (, , , ).^[3] The Dorian city of Knidos as well as a few Aegean islands, namely Paros, Thasos and Melos, chose the exact opposite innovation, using a broken-up circle for the short and a closed circle for the long /o/.^[3]

The name Ωμέγα is Byzantine; in Classical Greek, the letter was called ō (ὦ) (pronounced /ɔ̂ː/), whereas the omicron was called ou (οὖ) (pronounced /ôː/).^[4] 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.^[5]

In addition to the Greek alphabet, Omega was also adopted into the early Cyrillic alphabet (see Cyrillic omega (Ѡ, ѡ)). A Raetic variant is conjectured to be at the origin or parallel evolution of the Elder Futhark ᛟ.

Omega was also adopted into the Latin alphabet, as a letter of the 1982 revision to the African reference alphabet. It's in sparce use (see Latin omega).

The symbol Ω (uppercase letter)

Plaque in Kos with "underlined O" form of omega

The uppercase letter Ω is used as a symbol:

In chemistry:
- For oxygen-18, a natural, stable isotope of oxygen^[6]
- For omega loop, a protein structural motif consisting of a loop of six or more amino acid residues in any sequence, a structure named for its resemblance to the Greek letter.
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 U+2126 Ω OHM SIGN (HTML entity &ohm;), but it is included only for backward compatibility, and the canonically equivalent code point U+03A9 Ω GREEK CAPITAL LETTER OMEGA (Ω) is preferred.^[7]
- 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 average density of the universe, also called the density parameter.
- In astronomy (orbital mechanics), Ω refers to the longitude of the ascending node of an orbit.
In mathematics and computer science:
- In complex analysis, the Omega constant, a solution of Lambert's W function
- In differential geometry, the space of differential forms 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 subgroups 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 triangle geometry, Brocard points
- In number theory, Ω(n) is the number of prime divisors of n (counting multiplicity).^[8]
- In notation related to Big O notation to describe the asymptotic behavior of functions.
- Chaitin's constant.
- In set theory, the first infinite ordinal number, ω
- In set theory, the first uncountable ordinal number, ω₁ or Ω
As part of logo or trademark:
- The logo of Omega Watches SA
- 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 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, a Sonic the Hedgehog character.
- The logo of the Heroes of Olympus 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's Omega Mart in Area15, Las Vegas, Nevada
- The logo of Lalaji Memorial Omega International School

Omega-shaped entrance to the Panteón de la Cruz in Aguascalientes, representing the end of life.^[9]

Other:
- In eschatology, the symbol for the end of everything
- In molecular biology, the symbol is used as shorthand to signify a genetic construct introduced by a two-point crossover
- Omega Particle in the Star Trek universe
- The final form of NetNavi bosses in some of the Mega Man Battle Network games
- A secret boss in the Final Fantasy 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/EarthBound games
- A symbol used by U.S. citizens in the 1960s & 1970s to denote resistance to the U.S. war in Viet Nam. Adapted from the SI unit for electrical resistance.^[10]
- It's used along with Alpha in the Alpha and Omega, a Christian symbol.

The symbol ω (lowercase letter)

The minuscule letter ω is used as a symbol:

Biology, biochemistry and chemistry:
- In biochemistry, for one of the RNA polymerase subunits
- In biology, for fitness
- In chemistry, for denoting the carbon atom furthest from the carboxyl group of a fatty acid
- In genomics, as a measure of molecular evolution in protein-coding genes (also denoted as d_N/d_S or K_a/K_s ratio)
Physics:
- Angular velocity or angular frequency
- In computational fluid dynamics, the specific turbulence dissipation rate
- In meteorology, the change of pressure with respect to time of a parcel of air
- In circuit analysis and signal processing to represent angular frequency, related to frequency f by ω = 2πf
- In astronomy, 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 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 $\omega _{0}$ )
- In set theory, ω₁ is the first uncountable ordinal number^[11] (also sometimes written as Ω)
- A primitive root of unity, like the complex cube roots of 1
- The Wright Omega function
- A generic differential form
- 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 triangle geometry, a Brocard angle
- Clique number in Graph theory
Finance:
- In finance, the elasticity of options
- In analytical investment management, the tracking error of an investment manager
Other:
- Used in place of ん in Japanese typing shorthand.
- In linguistics, the phonological word
- In textual criticism, the archetype of a manuscript tradition
- In sociology, used to refer to the lowest ranking member of a group^[12]
- In shift_JIS art, used to represent the cat's mouth. (e.g. (´･ω･`) ｼｮﾎﾞｰﾝ)
- In actuarial sciences, used to represent the maximum life span that characterizes a mortality table

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