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**Mu** (uppercase **Μ**, lowercase **μ**; Ancient Greek μῦ [mŷː], Greek: μι or μυ—both [mi]) or **my**^{[1]} is the 12th letter of the Greek alphabet. In the system of Greek numerals it has a value of 40.^{[2]} 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. It is also used as coefficient of friction.

## Contents

## Names[edit]

### Ancient Greek[edit]

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

### Modern Greek[edit]

In Modern Greek, the letter is spelled μι and pronounced [mi]. In polytonic orthography, it is written with an acute accent: μί.^{[3]}^{[4]}

## Use as symbol[edit]

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[edit]

- 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.^{[5]} - the micron "μ", an old unit now named the micrometre and denoted "µm"

### Mathematics[edit]

"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 learning rate in artificial neural networks
- 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[edit]

In classical physics and engineering:

- the coefficient of friction (also used in aviation as braking coefficient)
- 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
^{[6]} - the electrical mobility of a charged particle
- a.k.a. rotor advance ratio, the ratio of aircraft airspeed to rotor tip speed in rotorcraft
^{[7]}^{[8]}

In particle physics:

- the elementary particles called the muon and antimuon

In thermodynamics:

- the chemical potential of a system or component of a system

### Computer science[edit]

- 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, is the type of lists with elements of type (a type variable): a sum of unit, representing
`nil`, with a pair of a and another (represented by ). In this notation, is a binding form, where the variable () introduced by is bound within the following term () to the term itself. Via substitution and arithmetic, the type expands to , an infinite sum of ever-increasing products of (that is, a is any -tuple of values of type for any ). Another way to express the same type is .

### Chemistry[edit]

In chemistry:

- the prefix given in IUPAC nomenclature for a bridging ligand

### Biology[edit]

In biology:

- the mutation rate in population genetics

### Pharmacology[edit]

In pharmacology:

- an important opiate receptor

### Orbital mechanics[edit]

- 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[edit]

- Mu major 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 in the name of the school idol group μ's, pronounced "muse", consisting of nine singing teen girls in the anime Love Live! School Idol Project
- Official fandom name of Kpop group f(x), appearing as either
**MeU**or 'µ'

### Cameras[edit]

The Olympus Corporation manufactures a series of digital cameras called Olympus µ [mju:]^{[9]} (known as Olympus Stylus in North America)

### Linguistics[edit]

In phonology, it often stands for mora. In syntax, μP (mu phrase) can be used as the name for a functional projection.^{[10]}. Celtic specialists sometimes use /µ/ to represent an Old Irish nasalized labial fricative of uncertain articulation, the ancestor of the sound represented by Modern Irish *mh*.

## Character encodings[edit]

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- Greek Mu / Coptic Mu
^{[11]}

Character | 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 | decimal | hex | decimal | hex | decimal | hex | decimal | 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 | 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 | decimal | hex | decimal | hex | decimal | hex | decimal | hex | decimal | 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 | 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 | decimal | hex | decimal | hex | decimal | 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[edit]

## See also[edit]

Look up or Μ in Wiktionary, the free dictionary.μ |

## References[edit]

**^**http://www.oed.com/view/Entry/123122**^**Hadley, James (1884).*A Greek Grammar for Schools and Colleges*. New York: American Book. p. 79.**^**http://e-library.iep.edu.gr/iep/collection/browse/item.html?code=01-17160&tab=02&start=40#i**^**http://e-library.iep.edu.gr/iep/collection/browse/item.html?code=01-18549&tab=01**^**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.**^**Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)