Mu (letter)

Mu /ˈm(j)uː/^[1]^[2] (uppercase Μ, lowercase μ; Ancient Greek μῦ [mŷː], Greek: μι or μυ—both [mi]) is the 12th letter of the Greek alphabet, representing the voiced bilabial nasal IPA: [m]. In the system of Greek numerals it has a value of 40.^[3] Mu was derived from the Egyptian hieroglyphic symbol for water, which had been simplified by the Phoenicians and named after their word for water, to become 𐤌^img (mem). Letters that derive from mu include the Roman M and the Cyrillic М.

Names

Ancient Greek

In Ancient Greek, the name of the letter was written μῦ and pronounced [mŷː]

Modern Greek

In Modern Greek, the letter is spelled μι and pronounced [mi]. In polytonic orthography, it is written with an acute accent: μί.^[4]^[5]

Use as symbol

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

Measurement

the SI prefix micro-, which represents one millionth, or 10⁻⁶. Lowercase letter "u" is often substituted for "μ" when the Greek character is not typographically available; for example the unit "microfarad", correctly "μF", is often rendered as "uF" or "ufarad" in technical documents.^[6]
the micron "μ", an old unit now named the micrometre and denoted "μm"

Mathematics

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

a measure in measure theory
minimalization in computability theory and Recursion theory
the integrating factor in ordinary differential equations
the degree of membership in a fuzzy set
the Möbius function in number theory
the population mean or expected value in probability and statistics
the Ramanujan–Soldner constant

Physics and engineering

In classical physics and engineering:

the coefficient of friction (also used in aviation as braking coefficient (see Braking action)
reduced mass in the two-body problem
Standard gravitational parameter in celestial mechanics
linear density, or mass per unit length, in strings and other one-dimensional objects
permeability in electromagnetism
the magnetic dipole moment of a current-carrying coil
dynamic viscosity in fluid mechanics
the amplification factor or voltage gain of a triode vacuum tube^[7]
the electrical mobility of a charged particle
the rotor advance ratio, the ratio of aircraft airspeed to rotor-tip speed in rotorcraft^[8]^[9]
the pore water pressure in saturated soil

In particle physics:

the elementary particles called the muon and antimuon
the proton-to-electron mass ratio

In thermodynamics:

the chemical potential of a system or component of a system

Computer science

In evolutionary algorithms:

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

In type theory:

Used to introduce a recursive data type. For example, ${\text{list}}(\tau )=\mu {}\alpha {}.1+\tau {}\alpha$ is the type of lists with elements of type $\tau$ (a type variable): a sum of unit, representing nil, 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-increasing products of $\tau$ (that is, a $\tau {}{\text{ list}}$ is any $k$ -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

In chemistry:

the prefix given in IUPAC nomenclature for a bridging ligand

Biology

In biology:

the mutation rate in population genetics
A class of Immunoglobulin heavy chain that defines IgM type Antibodies

Pharmacology

In pharmacology:

an important opiate receptor

Orbital mechanics

In orbital mechanics:

Standard gravitational parameter of a celestial body, the product of the gravitational constant G and the mass M
planetary discriminant, represents an experimental measure of the actual degree of cleanliness of the orbital zone, a criterion for defining a planet. 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 musician Mike Paradinas runs the label Planet 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 anime Love Live! School Idol Project
Official fandom name of Kpop group f(x), appearing as either MeU 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

The Olympus Corporation manufactures a series of digital cameras called Olympus μ [mju:]^[10] (known as Olympus Stylus in North America)

Linguistics

In phonology:

mora

In syntax:

μP (mu phrase) can be used as the name for a functional projection.^[11]

In Celtic linguistics:

/μ/ can represent an Old Irish nasalized labial fricative of uncertain articulation, the ancestor of the sound represented by Modern Irish mh.

Character encodings

Greek Mu / Coptic Mu^[12]

Character information
Preview	Μ		μ		µ		Ⲙ		ⲙ
Unicode name	GREEK CAPITAL LETTER MU		GREEK SMALL LETTER MU		MICRO SIGN		COPTIC CAPITAL LETTER MI		COPTIC SMALL LETTER MI
Encodings	decimal	hex	dec	hex	dec	hex	dec	hex	dec	hex
Unicode	924	U+039C	956	U+03BC	181	U+00B5	11416	U+2C98	11417	U+2C99
UTF-8	206 156	CE 9C	206 188	CE BC	194 181	C2 B5	226 178 152	E2 B2 98	226 178 153	E2 B2 99
Numeric character reference	Μ	Μ	μ	μ	µ	µ	Ⲙ	Ⲙ	ⲙ	ⲙ
Named character reference	Μ		μ		µ
ISO/IEC 8859-1					181	B5
ISO/IEC 8859-7	204	CC	236	EC
Code page 437, 850			230	E6	230	E6
Code page 737	139	8B	163	A3
Code page 851, 869	183	B7	230	E6
Code page 1253	204	CC	236	EC
Roman-8, Roman-9			243	F3	243	F3
TeX			\mu		\micro

Mathematical Mu

Character information
Preview	𝚳		𝛍		𝛭		𝜇		𝜧		𝝁
Unicode name	MATHEMATICAL BOLD CAPITAL MU		MATHEMATICAL BOLD SMALL MU		MATHEMATICAL ITALIC CAPITAL MU		MATHEMATICAL ITALIC SMALL MU		MATHEMATICAL BOLD ITALIC CAPITAL MU		MATHEMATICAL BOLD ITALIC SMALL MU
Encodings	decimal	hex	dec	hex	dec	hex	dec	hex	dec	hex	dec	hex
Unicode	120499	U+1D6B3	120525	U+1D6CD	120557	U+1D6ED	120583	U+1D707	120615	U+1D727	120641	U+1D741
UTF-8	240 157 154 179	F0 9D 9A B3	240 157 155 141	F0 9D 9B 8D	240 157 155 173	F0 9D 9B AD	240 157 156 135	F0 9D 9C 87	240 157 156 167	F0 9D 9C A7	240 157 157 129	F0 9D 9D 81
UTF-16	55349 57011	D835 DEB3	55349 57037	D835 DECD	55349 57069	D835 DEED	55349 57095	D835 DF07	55349 57127	D835 DF27	55349 57153	D835 DF41
Numeric character reference	𝚳	𝚳	𝛍	𝛍	𝛭	𝛭	𝜇	𝜇	𝜧	𝜧	𝝁	𝝁

Character information
Preview	𝝡		𝝻		𝞛		𝞵
Unicode name	MATHEMATICAL SANS-SERIF BOLD CAPITAL MU		MATHEMATICAL SANS-SERIF BOLD SMALL MU		MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL MU		MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL MU
Encodings	decimal	hex	dec	hex	dec	hex	dec	hex
Unicode	120673	U+1D761	120699	U+1D77B	120731	U+1D79B	120757	U+1D7B5
UTF-8	240 157 157 161	F0 9D 9D A1	240 157 157 187	F0 9D 9D BB	240 157 158 155	F0 9D 9E 9B	240 157 158 181	F0 9D 9E B5
UTF-16	55349 57185	D835 DF61	55349 57211	D835 DF7B	55349 57243	D835 DF9B	55349 57269	D835 DFB5
Numeric character reference	𝝡	𝝡	𝝻	𝝻	𝞛	𝞛	𝞵	𝞵

These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.

Image list for readers with font problems

^

References

^ "mu". The Chambers Dictionary (9th ed.). Chambers. 2003. ISBN 0-550-10105-5.
^ "mu". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating 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.
^ Albert Flack (19 April 2010). "US20130038341A1 - Contactor health monitor circuit and method". Google Patents. Retrieved 10 September 2018. Example of document using both "ufarad" and "microFarad"
^ 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
^ "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)

[1] "mu". The Chambers Dictionary (9th ed.). Chambers. 2003. ISBN 0-550-10105-5.

[2] "mu". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)

[3] Hadley, James (1884). A Greek Grammar for Schools and Colleges. New York: American Book. p. 79.

[4] Neoelliniki Grammatiki (Tis Dimotikis).

[5] Grammatiki tis Dimotikis Glossas.

[6] Albert Flack (19 April 2010). "US20130038341A1 - Contactor health monitor circuit and method". Google Patents. Retrieved 10 September 2018. Example of document using both "ufarad" and "microFarad"

[7] 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.

[8] "Nomenclature" NASA

[9] Definition

[10] "Olympus History : μ[mju:] (Stylus) Series".

[11] Johnson, Kyle (1991). "Object Positions". Natural Language and Linguistic Theory. 9 (4): 577–636. doi:10.1007/BF00134751. S2CID 189901613.

[12] Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)

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