Mu (letter)

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

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

"μ" is used as a unit prefix denoting a factor of 10⁻⁶ (one millionth), in this context, the symbol's name is "micro". It is the only unit prefix that is not composed of Latin letters.

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

"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 ^[6]
• The Möbius function in number theory ^{[7] [8]}
• The population mean or expected value in probability and statistics ^[9]
• The service or departure rate in queueing theory ^[10]
• The Ramanujan–Soldner constant ^[11]

In classical physics and engineering:

• The coefficient of friction ^[12] (also used in aviation as braking coefficient (see Braking action))
• Reduced mass in the two-body problem ^[13]
• Standard gravitational parameter in celestial mechanics^[14]
• Linear density, or mass per unit length, in strings and other one-dimensional objects^[15]
• Permeability in electromagnetism^[16]
• The magnetic dipole moment of a current-carrying coil ^[17]
• Dynamic viscosity in fluid mechanics
• The amplification factor or voltage gain of a triode vacuum tube ^[18]
• The electrical mobility of a charged particle
• The rotor advance ratio, the ratio of aircraft airspeed to rotor-tip speed in rotorcraft ^{[19] [20]}
• The pore water pressure in saturated soil
• The shear modulus in solid mechanics

In particle physics:

• Elementary particles: muon and antimuon (μ⁻
  , μ⁺
  ), muon neutrino and antineutrino (ν
  _μ, ν
  _μ)
• The proton-to-electron mass ratio ^[21]

In thermodynamics:

• The chemical potential of a system or component of a system

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

In chemistry:

• The prefix given in IUPAC nomenclature for a bridging ligand

In biology:

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

In pharmacology:

• An important opiate receptor

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.

• 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.

The Olympus Corporation manufactures a series of digital cameras called Olympus μ [mju:]^[22] (known as Olympus Stylus in North America).

In phonology:

• Mora

In syntax:

• μP (mu phrase) can be used as the name for a functional projection.^[23]

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.