Mu ( / ˈ m ( j ) uː / ; uppercase Μ , lowercase μ ; Ancient Greek μῦ [mŷː] , Greek : μι or μυ—both [mi] ) is the 12th letter of the Greek alphabet. It represents the sound made by pressing the lips together, shown in the International Phonetic Alphabet as [m]. In the Greek numeral system, Mu has a value of 40. The letter Mu was created from an Egyptian picture symbol for water. The Phoenicians simplified this symbol and named it "mem" after their word for water. Other letters based on Mu include the Latin letter M and the Cyrillic letter М. The lowercase form of Mu looks similar to the lowercase Latin letter U (u).

Names

In ancient Greek, the letter was written as μῦ and pronounced [mŷː]. Today, the letter is spelled μι and pronounced [mi]. In a special writing system called polytonic orthography, the letter is written with an acute accent: μί.

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 looks the same as the Latin letter M.

"μ" is used as a unit prefix meaning a factor of one millionth. In this context, the symbol's name is "micro." It is the only unit prefix that is not made from Latin letters.

• "Micro" is an International System of Units (SI) prefix.
• The micrometre, written as "μm," is also called "micron" in non-SI terms.

"μ" is conventionally used to represent certain concepts; 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 service or departure rate in queueing theory
• The Ramanujan–Soldner constant

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
• 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
• The shear modulus in solid mechanics

In particle physics:

• Elementary particles: muon and antimuon (μ, μ), muon neutrino and antineutrino (νμ, νμ)
• The proton-to-electron mass ratio

• 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)

• Used to introduce a recursive data type. For example, list(τ) = μα.1 + τα is the type of lists with elements of type τ (a type variable): a sum of unit, representing nil, with a pair of a τ and another list(τ) (represented by α). In this notation, μ is a binding form, where the variable (α) introduced by μ is bound within the following term (1 + τα) to the term itself. Via substitution and arithmetic, the type expands to 1 + τ + τ² + τ³ + ⋯, an infinite sum of ever-increasing products of τ (that is, a τ list is any k-tuple of values of type τ for any k ≥ 0). Another way to express the same type is list(τ) = 1 + τ list(τ).

• The prefix given in IUPAC nomenclature for a bridging ligand

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

• 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 uses 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:] (known as Olympus Stylus in North America).

• Mora

• 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.

Unicode

The lowercase mu, which is also called the micro sign, was found at 0xB5 in the 8-bit ISO-8859-1 encoding. This encoding was used by Unicode and many other systems. It was also located at 0xE6 in the CP437 encoding used on IBM PCs. Unicode identifies mu as the version that works with the micro sign.

• U+00B5 µ MICRO SIGN ( µ )
• U+039C Μ GREEK CAPITAL LETTER MU ( Μ )
• U+03BC μ GREEK SMALL LETTER MU ( μ )
• U+2C98 Ⲙ COPTIC CAPITAL LETTER MI
• U+2C99 ⲙ COPTIC SMALL LETTER MI
• U+1D6B3 𝚳 MATHEMATICAL BOLD CAPITAL MU
• U+1D6CD 𝛍 MATHEMATICAL BOLD SMALL MU
• U+1D6ED 𝛭 MATHEMATICAL ITALIC CAPITAL MU
• U+1D707 𝜇 MATHEMATICAL ITALIC SMALL MU
• U+1D727 𝜧 MATHEMATICAL BOLD ITALIC CAPITAL MU
• U+1D741 𝝁 MATHEMATICAL BOLD ITALIC SMALL MU
• U+1D761 𝝡 MATHEMATICAL SANS-SERIF BOLD CAPITAL MU
• U+1D77B 𝝻 MATHEMATICAL SANS-SERIF BOLD SMALL MU
• U+1D79B 𝞛 MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL MU
• U+1D7B5 𝞵 MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL MU