# Mu (letter)

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Mu (uppercase Μ, lowercase μ; Ancient Greek μῦ [mŷː], Greek: μι or μυ—both [mi]) or my[1] is the 12th letter of the Greek alphabet. In the system of Greek numerals it has a value of 40.[2] 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.

## Names

### Ancient Greek

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

### Modern Greek

In Modern Greek, the letter is spelled μι and pronounced [mi]. In monotonic orthography, the ancient version is written with an acute accent instead of a circumflexμύ.

## 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.[3]
• 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.

### Computer science

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

In chemistry:

### Biology

In biology:

• the mutation rate in population genetics

In pharmacology:

### Music

• Mu major 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 in the name of the school idol group μ's, pronounced "muse", consisting of nine singing teen girls in the anime Love Live! School Idol Project
• Official fandom name of Kpop group f(x), appearing as either MeU or 'µ'

### Cameras

The Olympus Corporation manufactures a series of digital cameras called Olympus µ[mju:][7] (known as Olympus Stylus in North America)

### Linguistics

In phonology, it often stands for mora. In syntax, μP (mu phrase) can be used as the name for a functional projection.[8]. Celtic specialists sometimes use /µ/ to 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 Mu[9]
Character Μ μ µ
Unicode name GREEK CAPITAL LETTER MU GREEK SMALL LETTER MU MICRO SIGN COPTIC CAPITAL LETTER MI COPTIC SMALL LETTER MI
Encodings decimal hex decimal hex decimal hex decimal hex decimal hex
Unicode 924 U+039C 956 U+03BC 181 U+00B5 11416 U+2C98 11417 U+2C99
UTF-8 206 156 CE 9C 206 188 CE BC 194 181 C2 B5 226 178 152 E2 B2 98 226 178 153 E2 B2 99
Numeric character reference &#924; &#x39C; &#956; &#x3BC; &#181; &#xB5; &#11416; &#x2C98; &#11417; &#x2C99;
Named character reference &Mu; &mu; &micro;
ISO/IEC 8859-1 181 B5
ISO/IEC 8859-7 204 CC 236 EC
Code page 437, 850 230 E6 230 E6
Code page 737 139 8B 163 A3
Code page 851, 869 183 B7 230 E6
Code page 1253 204 CC 236 EC
Roman-8, Roman-9 243 F3 243 F3
TeX \mu \micro
• Mathematical Mu
Character 𝚳 𝛍 𝛭 𝜇 𝜧 𝝁
Unicode name MATHEMATICAL BOLD
CAPITAL MU
MATHEMATICAL BOLD
SMALL MU
MATHEMATICAL ITALIC
CAPITAL MU
MATHEMATICAL ITALIC
SMALL MU
MATHEMATICAL BOLD ITALIC
CAPITAL MU
MATHEMATICAL BOLD ITALIC
SMALL MU
Encodings decimal hex decimal hex decimal hex decimal hex decimal hex decimal hex
Unicode 120499 U+1D6B3 120525 U+1D6CD 120557 U+1D6ED 120583 U+1D707 120615 U+1D727 120641 U+1D741
UTF-8 240 157 154 179 F0 9D 9A B3 240 157 155 141 F0 9D 9B 8D 240 157 155 173 F0 9D 9B AD 240 157 156 135 F0 9D 9C 87 240 157 156 167 F0 9D 9C A7 240 157 157 129 F0 9D 9D 81
UTF-16 55349 57011 D835 DEB3 55349 57037 D835 DECD 55349 57069 D835 DEED 55349 57095 D835 DF07 55349 57127 D835 DF27 55349 57153 D835 DF41
Numeric character reference &#120499; &#x1D6B3; &#120525; &#x1D6CD; &#120557; &#x1D6ED; &#120583; &#x1D707; &#120615; &#x1D727; &#120641; &#x1D741;
Character 𝝡 𝝻 𝞛 𝞵
Unicode name MATHEMATICAL SANS-SERIF
BOLD CAPITAL MU
MATHEMATICAL SANS-SERIF
BOLD SMALL MU
MATHEMATICAL SANS-SERIF
BOLD ITALIC CAPITAL MU
MATHEMATICAL SANS-SERIF
BOLD ITALIC SMALL MU
Encodings decimal hex decimal hex decimal hex decimal hex
Unicode 120673 U+1D761 120699 U+1D77B 120731 U+1D79B 120757 U+1D7B5
UTF-8 240 157 157 161 F0 9D 9D A1 240 157 157 187 F0 9D 9D BB 240 157 158 155 F0 9D 9E 9B 240 157 158 181 F0 9D 9E B5
UTF-16 55349 57185 D835 DF61 55349 57211 D835 DF7B 55349 57243 D835 DF9B 55349 57269 D835 DFB5
Numeric character reference &#120673; &#x1D761; &#120699; &#x1D77B; &#120731; &#x1D79B; &#120757; &#x1D7B5;

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.

1. ^

## References

1. ^ http://www.oed.com/view/Entry/123122
2. ^ Hadley, James (1884). A Greek Grammar for Schools and Colleges. New York: American Book. p. 79.
3. ^ Albert Flack (19 April 2010). "US20130038341A1 - Contactor health monitor circuit and method". Google Patents. Retrieved 10 September 2018. Example of document using both "ufarad" and "microFarad"
4. ^ 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.
5. ^
6. ^ Definition
7. ^ Olympus History : µ[mju:] (Stylus) Series
8. ^ Johnson, Kyle (1991). "Object Positions". Natural Language and Linguistic Theory. 9 (4): 577–636. doi:10.1007/BF00134751.
9. ^ Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)