Mu (letter)

Mu (uppercase Μ, lowercase μ; Ancient Greek , ell, μι or μυ—both ) is the 12th letter of the Greek alphabet, representing the voiced bilabial nasal . In the system of Greek numerals it has a value of 40. 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 (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 and pronounced

Modern Greek

In Modern Greek, the letter is spelled and pronounced . In polytonic orthography, it is written with an acute accent: .

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.
*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 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
*the electrical mobility of a charged particle
*the rotor advance ratio, the ratio of aircraft airspeed to rotor-tip speed in rotorcraft
*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, $\text(\tau) = \mu\alpha.1 + \tau\alpha$ is the type of lists with elements of type $\tau$ (a type variable): a sum of unit, representing , with a pair of a $\tau$ and another $\text(\tau)$ (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 $\tau\text$ is any $k$-tuple of values of type $\tau$ for any $k \ge 0$). Another way to express the same type is $\text(\tau) = 1 + \tau\text(\tau)$.

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 (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.

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 MuUnicode Code Charts
Greek and Coptic (Range: 0370-03FF)
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* Mathematical Mu

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

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See also

* Greek letters used in mathematics, science, and engineering
* Fraser alphabet#Consonants

References

{{Reflist

Greek letters