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Mu (letter)

From Wikipedia, the free encyclopedia

Mu (/ˈm(j)/;[1][2] uppercase Μ, lowercase μ; Ancient Greek μῦ [mŷː], Greek: μι or μυ—both [mi]) is the twelfth letter of the Greek alphabet, representing the voiced bilabial nasal IPA: [m]. In the system of Greek numerals it has a value of 40.[3] 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 𐤌img (mem). Letters that derive from mu include the Roman M and the Cyrillic М, though the lowercase resembles a small Latin U (u).

Greek letter mu

Names

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Ancient Greek

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

Modern Greek

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In Modern Greek, the letter is spelled μι and pronounced [mi]. In polytonic orthography, it is written with an acute accentμί.[4][5]

Use as symbol

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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

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"μ" is used as a unit prefix denoting a factor of 10−6 (one millionth), in this context, the symbol's name is "micro".

Mathematics

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"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

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In classical physics and engineering:

In particle physics:

In thermodynamics:

Computer science

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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 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

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In chemistry:

Biology

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In biology:

Pharmacology

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In pharmacology:

Orbital mechanics

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In orbital mechanics:

Music

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  • 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

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

Linguistics

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In phonology:

In syntax:

  • μP (mu phrase) can be used as the name for a functional projection.[10]

In Celtic linguistics:

Unicode

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The lower-case mu (as "micro sign") appeared at 0xB5 in the 8-bit ISO-8859-1 encoding, from which Unicode and many other encodings inherited it. It was also at 0xE6 in the popular CP437 on the IBM PC. Unicode has declared that a "real" mu is different than the micro sign.[11]

  • U+00B5 µ MICRO SIGN (µ)
  • U+039C Μ GREEK CAPITAL LETTER MU (Μ)
  • U+03BC μ GREEK SMALL LETTER MU (μ)
  • U+2C98 COPTIC CAPITAL LETTER MI
  • U+2C99 COPTIC SMALL LETTER MI

These are only to be used for mathematical text, not for text styling:

  • 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

See also

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References

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  1. ^ "mu". The Chambers Dictionary (9th ed.). Chambers. 2003. ISBN 0-550-10105-5.
  2. ^ "mu". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
  3. ^ Hadley, James (1884). A Greek Grammar for Schools and Colleges. New York: American Book. p. 79.
  4. ^ Neoelliniki Grammatiki (Tis Dimotikis).
  5. ^ Grammatiki tis Dimotikis Glossas.
  6. ^ 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 (Vg) of the tube.
  7. ^ "Nomenclature" NASA
  8. ^ "Definition".
  9. ^ "Olympus History : μ[mju:] (Stylus) Series".
  10. ^ Johnson, Kyle (1991). "Object Positions". Natural Language and Linguistic Theory. 9 (4): 577–636. doi:10.1007/BF00134751. S2CID 189901613.
  11. ^ Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)