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Mu (letter)

Mu (; uppercase Μ, lowercase μ; Ancient Greek , 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 the letter mem (𐤌). Letters that derive from mu include the Latin M and the Cyrillic М, though the lowercase resembles a small Latin U (u).

Names

Ancient Greek

In 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.

Prefix for units of measurement

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

Mathematics

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

Physics and engineering

In classical physics and engineering:

In particle physics:

In thermodynamics:

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, is the type of lists with elements of type (a type variable): a sum of unit, representing , 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

In chemistry:

Biology

In biology:

Pharmacology

In pharmacology:

Orbital mechanics

In orbital mechanics:

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:

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.

Unicode

The lowercase mu (as "micro sign") appeared at in the 8-bit ISO-8859-1 encoding, from which Unicode and many other encodings inherited it. It was also at in the popular CP437 on the IBM PC. Unicode designates mu as is the compatibility equivalent of the micro sign.

See also

References