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Mu (letter)

From Wikipedia, the free encyclopedia

Twelfth letter of the Greek alphabet

For other uses, seeMU.

Not to be confused withNu (letter),M, orEm (Cyrillic).

"µ" redirects here. For the micro sign, seeMicro-.

Αα	Alpha	Νν	Nu
Ββ	Beta	Ξξ	Xi
Γγ	Gamma	Οο	Omicron
Δδ	Delta	Ππ	Pi
Εε	Epsilon	Ρρ	Rho
Ζζ	Zeta	Σσς	Sigma
Ηη	Eta	Ττ	Tau
Θθ	Theta	Υυ	Upsilon
Ιι	Iota	Φφ	Phi
Κκ	Kappa	Χχ	Chi
Λλ	Lambda	Ψψ	Psi
Μμ	Mu	Ωω	Omega

Archaic local variants

Ϝϝ	Digamma	Ͱͱ	Heta
Ϻϻ	San	Ϙϙ	Koppa
Ͷͷ	Tsan Digamma	Ͳͳ	Sampi
Ϸϸ	Sho

Diacritics and other symbols

Numerals (Attic)

Related topics

Category

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Mu, ormy (/ˈm(j)uː/ ^ⓘ;^[1]^[2] uppercaseΜ, lowercaseμ;Ancient Greekμῦ[mŷː],Greek:μι or μυ—both[mi]), is the twelfthletter of theGreek alphabet, representing thevoiced bilabial nasalIPA:[m]. In the system ofGreek numerals it has a value of 40.^[3] Mu was derived from theEgyptian hieroglyphic symbol for water, which had been simplified by thePhoenicians and named after their word for water, to become𐤌^img (mem). Letters that derive from mu include theRoman M and theCyrillic М, though the lowercase resembles a smallLatin U (u).

Greek letter mu

Names

Ancient Greek

In Greek, the name of the letter was writtenμῦ and pronounced[mŷː].

Modern Greek

InModern Greek, the letter is spelledμι and pronounced[mi]. In polytonic orthography, it is written with anacute accent: μί.^[4]^[5]

Use as symbol

The lowercase letter mu (μ) is used as a special symbol in manyacademic fields. Uppercase mu is not used, because it appears identical to LatinM.

Prefix for units of measurement

"μ" is used as aunit prefix denoting a factor of 10⁻⁶ (onemillionth), in this context, the symbol's name is "micro".

Metric prefix
International System of Units prefix, also known as "SI prefix"
The micrometre with a symbol of "μm" can also be referred to as the non-SI term "micron".

Mathematics

"μ" is conventionally used to denote certain things; however, any Greek letter or other symbol may be used freely as a variable name.

ameasure inmeasure theory
minimalization incomputability theory andRecursion theory
theintegrating factor inordinary differential equations
the degree ofmembership in afuzzy set^[6]
theMöbius function innumber theory^[7]^[8]
the populationmean orexpected value inprobability andstatistics^[9]
theRamanujan–Soldner constant^[10]

Physics and engineering

Inclassical physics andengineering:

thecoefficient of friction^[11] (also used in aviation as braking coefficient (seeBraking action))
reduced mass in thetwo-body problem^[12]
Standard gravitational parameter in celestial mechanics^[13]
linear density, or mass per unit length, in strings and other one-dimensional objects^[14]
permeability in electromagnetism^[15]
themagnetic dipole moment of acurrent-carryingcoil
dynamic viscosity in fluid mechanics
theamplification factor orvoltage gain of atriode vacuum tube^[16]
theelectrical mobility of a charged particle
therotor advance ratio, the ratio of aircraftairspeed to rotor-tip speed inrotorcraft^[17]^[18]
thepore water pressure in saturated soil

Inparticle physics:

the elementary particles called themuon and antimuon
theproton-to-electron mass ratio^[19]

Inthermodynamics:

thechemical potential of a system or component of a system

Computer science

Inevolutionary algorithms:

μ, population size from which in each generation λ offspring will generate (the terms μ and λ originate fromevolution strategy notation)

Used to introduce arecursive data type. For example, ${\text{list}}(\tau )=\mu {}\alpha {}.1+\tau {}\alpha$ is the type of lists with elements of type $\tau$ (atype variable): asum ofunit, representingnil, with a pair of a $\tau$ and another ${\text{list}}(\tau )$ (represented by $\alpha$ ). In this notation, $\mu$ is a binding form, where the variable ( $\alpha$ ) introduced by $\mu$ is bound within the following term ( $1+\tau {}\alpha$ ) to the term itself. Via substitution and arithmetic, the type expands to $1+\tau +\tau ^{2}+\tau ^{3}+\cdots$ , an infinite sum of ever-increasingproducts of $\tau$ (that is, a $\tau {}{\text{ list}}$ is any $k {\displaystyle k}$ -tuple of values of type $\tau$ for any $k\geq 0$ ). Another way to express the same type is ${\text{list}}(\tau )=1+\tau {}{\text{list}}(\tau )$ .

Chemistry

the prefix given inIUPAC nomenclature for abridging ligand

Biology

themutation rate in population genetics
A class ofImmunoglobulin heavy chain that definesIgM typeAntibodies

Pharmacology

Inpharmacology:

an importantopiate receptor

Orbital mechanics

Inorbital mechanics:

Standard gravitational parameter of acelestial body, the product of thegravitational constantG and themassM
planetary discriminant, represents an experimental measure of the actual degree ofcleanliness of the orbital zone, acriterion fordefining aplanet. The value of μ is calculated by dividing the mass of the candidate body by the total mass of the other objects that share its orbital zone.

Music

Mu chord
Electronic musicianMike Paradinas runs the labelPlanet Mu which utilizes the letter as its logo, and releases music under the pseudonym μ-Ziq, pronounced "music"
Used as the name of the school idol group μ's, pronounced "muse", consisting of nine singing idols in the animeLove Live! School Idol Project
Officialfandom name of Kpop groupf(x), appearing as eitherMeU or 'μ'
Hip-hop artist Muonboy has taken inspiration from the particle for his stage name and his first EP named Mu uses the letter as its title.

Cameras

TheOlympus Corporation manufactures a series of digital cameras called Olympus μ[mju:]^[20] (known asOlympus Stylus in North America).

Linguistics

mora

μP (mu phrase) can be used as the name for a functional projection.^[21]

InCeltic linguistics:

/μ/ can represent anOld Irish nasalized labialfricative of uncertain articulation, the ancestor of the sound represented byModern Irishmh.

Unicode

The lowercase mu (as "micro sign") appeared at0xB5 in the 8-bitISO-8859-1 encoding, from which Unicode and many other encodings inherited it. It was also at0xE6 in the popularCP437 on the IBM PC. Unicode designates mu as is thecompatibility equivalent of the micro sign.^[22]

U+00B5 µMICRO SIGN (µ)
U+039C ΜGREEK CAPITAL LETTER MU (Μ)
U+03BC μGREEK SMALL LETTER MU (μ)
U+2C98 ⲘCOPTIC CAPITAL LETTER MI
U+2C99 ⲙCOPTIC SMALL LETTER MI
U+1D6B3 𝚳MATHEMATICAL BOLD CAPITAL MU^[a]
U+1D6CD 𝛍MATHEMATICAL BOLD SMALL MU
U+1D6ED 𝛭MATHEMATICAL ITALIC CAPITAL MU
U+1D707 𝜇MATHEMATICAL ITALIC SMALL MU
U+1D727 𝜧MATHEMATICAL BOLD ITALIC CAPITAL MU
U+1D741 𝝁MATHEMATICAL BOLD ITALIC SMALL MU
U+1D761 𝝡MATHEMATICAL SANS-SERIF BOLD CAPITAL MU
U+1D77B 𝝻MATHEMATICAL SANS-SERIF BOLD SMALL MU
U+1D79B 𝞛MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL MU
U+1D7B5 𝞵MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL MU

^TheMATHEMATICAL symbols are only for math. Stylized text should use markup.

See also

Look upΜ orμ in Wiktionary, the free dictionary.

References

^"mu".The Chambers Dictionary (9th ed.). Chambers. 2003.ISBN 0-550-10105-5.
^"mu".Oxford English Dictionary (Online ed.).Oxford University Press. (Subscription orparticipating institution membership required.)
^Hadley, James (1884).A Greek Grammar for Schools and Colleges. New York: American Book. p. 79.
^Neoelliniki Grammatiki (Tis Dimotikis).
^Grammatiki tis Dimotikis Glossas.
^Chaira, Tamalika (2019).Fuzzy set and its extension: the intuitionistic fuzzy set. Hoboken, NJ: Wiley. p. 3.ISBN 978-1-119-54419-7.If X be a collection of objects denoted by X, then a fuzzy set A in X is defined as:… where μ_A X is the degree of membership of X in A.
^Weisstein, Eric W."Möbius Function".mathworld.wolfram.com. Retrieved2025-01-24.
^"DLMF: §27.2 Functions ‣ Multiplicative Number Theory ‣ Chapter 27 Functions of Number Theory".dlmf.nist.gov. Retrieved2025-01-31.
^Weisstein, Eric W."Mean".mathworld.wolfram.com. Retrieved2025-01-24.
^Weisstein, Eric W."Soldner's Constant".mathworld.wolfram.com. Retrieved2025-01-31.Soldner's constant, denoted μ (or sometimes c)...
^Dante, Roberto C. (2016).Handbook of friction materials and their applications. Woodhead Publishing in materials. Cambridge: Woodhead Publishing. p. 2.ISBN 978-0-08-100619-1.In the case of dry friction w(X) is the coefficient of friction μ, which is affected by temperature speed and other variables…
^Kulp, Christopher W.; Pagonis, Vasilis (2021).Classical mechanics: a computational approach with examples using mathematica and Python (1st ed.). Boca Raton, FL: CRC Press.ISBN 978-1-138-49528-9.The single massμ is called thereduced mass of the two-body system and represents an effective inertial mass appearing in the two-body problem.
^Dodd, Richard (2012).Using SI units in astronomy. Cambridge: Cambridge University Press. p. 96.ISBN 978-0-521-76917-4.The standard gravitational parameter μ, is the product of the Newtonian gravitational constant G, and the mass of a given celestial body.
^Walker, Jearl; Resnick, Robert; Halliday, David (2014).Halliday & Resnick fundamentals of physics (10th ed.). Hoboken, NJ: Wiley. p. 452.ISBN 978-1-118-23376-4.We call this ratio thelinear density μ of the striing.
^Jiles, David (2016).Introduction to magnetism and magnetic materials (Third ed.). Boca Raton London New York: CRC Press, Taylor & Francis Group. p. 42.ISBN 978-1-138-44149-1.We can now make a general statement for the permeabilityμ and susceptibilityχ
^Ballou, Glen (1987).Handbook for Sound Engineers: The New Audio Cyclopedia (1 ed.). Howard W. Sams Co. p. 250.ISBN 0-672-21983-2.Amplification factor or voltage gain is the amount the signal at the control grid is increased in amplitude after passing through the tube, which is also referred to as the Greek letter μ (mu) or voltage gain (V_g) of the tube.
^"Nomenclature"NASA
^"Definition".
^Thompson, Rodger I. (2017)."Fundamental constants as monitors of the universe".MG14. WORLD SCIENTIFIC:3657–3663.arXiv:1602.03192.doi:10.1142/9789813226609_0476.ISBN 978-981-322-659-3.There are now observational constraints on the time variation of the proton to electron mass ratio μ at the 10−7 level.
^"Olympus History : μ[mju:] (Stylus) Series".
^Johnson, Kyle (1991). "Object Positions".Natural Language and Linguistic Theory.9 (4):577–636.doi:10.1007/BF00134751.S2CID 189901613.
^Unicode Code Charts:Greek and Coptic (Range: 0370-03FF)

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