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# Latin alphabet

The Latin alphabet is used, with modifications, to write all languages directly derived from Latin (such as French and Italian), languages with much Latin influence (such as English), some Slavic languages (such as Polish and Slovene) and even some Asian languages with no Latin influence in their formative period (such as Vietnamese).

Almost all languages that use the Latin alphabet also use diacritical marks (accents) for some of the letters; English is a notable exception to this. The use of diacritical marks in mathematical notation is rare; authors who declare they use accents in their mathematical notation are usually referring to an apostrophe or prime symbol, e.g. ${\displaystyle \scriptstyle a^{\prime }\,=\,(a_{1}^{\prime },\,\ldots ,\,a_{n}^{\prime })\,}$.[1]

The Latin alphabet and its usage for mathematical symbols
Letter Constants Functions Variables Miscellaneous
${\displaystyle A\,}$ Artin's constant ${\displaystyle \scriptstyle A(x)\,}$ The generating function for a sequence[2]

● An angle
● Area of a 2-dimensional figure

${\displaystyle \scriptstyle \mathbb {A} \,}$ Algebraics (set of algebraic numbers) [3]
${\displaystyle \scriptstyle \mathbb {A} \,}$ Algebraic integers of ${\displaystyle \scriptstyle \mathbb {Q} ({\sqrt {m}})\,}$[4]
${\displaystyle \scriptstyle \mathbb {A} \,}$ Affine space, or the ring of adeles
${\displaystyle \scriptstyle \forall \,}$ Universal quantifier (a logical quantifier)

${\displaystyle a\,}$ ${\displaystyle \scriptstyle a(n)\,}$ The ${\displaystyle \scriptstyle n\,}$th term of a sequence[5]

Real part of a complex number
● A point in a Euclidean space ${\displaystyle \scriptstyle \mathbb {R} ^{n}\,}$[6]
● A side[7]

${\displaystyle B\,}$ Brun's constant[8] ${\displaystyle \scriptstyle B_{k}\,}$ Bernoulli number[9] ● An angle related in some way to ${\displaystyle \scriptstyle A\,}$

${\displaystyle \scriptstyle \mathbb {B} \,}$ Booleans[3]
${\displaystyle \scriptstyle \mathbb {B} ^{n}\,}$ ${\displaystyle \scriptstyle n\,}$-ball[3]
${\displaystyle \scriptstyle \mathbb {B} \,}$ set of norms of nonzero elements of ${\displaystyle \scriptstyle \mathbb {A} (m)\,}$[4]
${\displaystyle \scriptstyle {\mathcal {B}}^{d}\,}$ Borel ${\displaystyle \scriptstyle \sigma \,}$-algebra of ${\displaystyle \scriptstyle \mathbb {R} ^{d}\,}$[10]

${\displaystyle b\,}$

${\displaystyle \scriptstyle bi\,}$ or ${\displaystyle \scriptstyle ib\,}$ Imaginary part of a complex number
● A point in a Euclidean space ${\displaystyle \scriptstyle \mathbb {R} ^{n}\,}$[6]
● A side[11]

${\displaystyle C\,}$

${\displaystyle \scriptstyle C_{n}\,}$ The ${\displaystyle \scriptstyle n\,}$th Catalan number[12]
${\displaystyle \scriptstyle C(n,k)\,}$ Binomial coefficient[13]

● The third angle in a triangle or a quadrangle

${\displaystyle \scriptstyle \mathbb {C} \,}$ The set of complex numbers[14]
${\displaystyle \scriptstyle \mathbb {C} ^{*}\,}$ The set of complex numbers, excluding 0.
${\displaystyle \scriptstyle \mathbb {C} _{-}\,=\,\mathbb {C} \setminus \{x\in \mathbb {R} ;x\leq 0\}\,}$ Slit plane along the negative real half-line[15]
${\displaystyle \scriptstyle \mathbb {C} ^{\bullet }\,=\,\mathbb {C} \setminus \{0\}\,}$ Punctured plane[15]
${\displaystyle \scriptstyle {\overline {\mathbb {C} }}\,=\,\mathbb {C} \cup \{\infty \}\,}$ Riemann sphere[15]
${\displaystyle \scriptstyle \mathbb {C} P^{n}\,}$ The ${\displaystyle \scriptstyle n\,}$-dimensional complex projective space[3]
${\displaystyle \scriptstyle P^{n}(\mathbb {C} )\,}$ The ${\displaystyle \scriptstyle n\,}$-dimensional complex projective space[15]

${\displaystyle c\,}$ ● The speed of light in Einstein's famous formula ● A point in a Euclidean space ${\displaystyle \scriptstyle \mathbb {R} ^{n}\,}$[6]
${\displaystyle D\,}$ ● The fourth angle in a guadrangle

${\displaystyle \scriptstyle \mathbb {D} ^{n}\,}$ ${\displaystyle \scriptstyle n\,}$-disk[3]
${\displaystyle \scriptstyle \mathbb {D} \,}$ ring of integral quaternions[4]

${\displaystyle d\,}$

${\displaystyle \scriptstyle d(\Lambda )\,}$ Determinant of a lattice[16]
${\displaystyle \scriptstyle d\,}$ Discriminant of a quadratic integer ring or a quadratic number field
${\displaystyle \scriptstyle d(n)\,}$ Number of divisors of ${\displaystyle \scriptstyle n\,}$ (usual notation is ${\displaystyle \scriptstyle \sigma _{0}(n)\,}$)[17]

Divisor of an integer
● A point in a Euclidean space ${\displaystyle \scriptstyle \mathbb {R} ^{n}\,}$[6]

${\displaystyle E\,}$

${\displaystyle \scriptstyle \mathbb {E} ^{n}\,}$ ${\displaystyle \scriptstyle n\,}$-dimensional Euclidean space[3]
${\displaystyle \scriptstyle \exists \,}$ Existential quantifier (a logical quantifier)
${\displaystyle \scriptstyle \exists !\,}$ Uniqueness quantifier (a logical quantifier)

${\displaystyle e\,}$ Euler's number ${\displaystyle \scriptstyle e\,\approx \,2.718\,}$[18] ${\displaystyle \scriptstyle e_{n}\,}$ The ${\displaystyle \scriptstyle n\,}$th member of the Sylvester sequence ● A point in a Euclidean space ${\displaystyle \scriptstyle \mathbb {R} ^{n}\,}$[6]
${\displaystyle F\,}$

${\displaystyle \scriptstyle F_{n}\,}$ The ${\displaystyle \scriptstyle n\,}$th Fibonacci number[19]
${\displaystyle \scriptstyle F_{n}\,}$ The ${\displaystyle \scriptstyle n\,}$th Fermat number ${\displaystyle \scriptstyle 2^{2^{n}}\,}$[20]

${\displaystyle \scriptstyle \mathbb {F} _{p}\,}$ Finite field with ${\displaystyle \scriptstyle p\,}$ elements[21]
${\displaystyle f\,}$

${\displaystyle \scriptstyle f(x)\,}$ A function
${\displaystyle \scriptstyle f_{n}\,}$ Alternate notation for the ${\displaystyle \scriptstyle n\,}$th Fermat number ${\displaystyle \scriptstyle 2^{2^{n}}\,}$ (to distinguish from Fibonacci numbers)[22]
${\displaystyle \scriptstyle f(x)\,}$ A distance function of a convex or star body[6]

${\displaystyle G\,}$ ${\displaystyle \scriptstyle \mathbb {G} \,}$ Gaussian integers[3]
${\displaystyle g\,}$

${\displaystyle \scriptstyle g(x)\,}$ A function related in some way to ${\displaystyle \scriptstyle f(x)\,}$
${\displaystyle \scriptstyle g(x)\,}$ A function of a convex or star body[6]

${\displaystyle H\,}$ ${\displaystyle \scriptstyle H(n)\,}$ Harmonic mean of divisors of ${\displaystyle \scriptstyle n\,}$[23]

${\displaystyle \scriptstyle \mathbb {H} \,}$ Quaternions, upper half-lane[3]
${\displaystyle \scriptstyle \mathbb {H} ^{2}\,}$ Hyperbolic plane[3]
${\displaystyle \scriptstyle \mathbb {H} \,}$ Division ring of rational quaternions[4]

${\displaystyle h\,}$ ${\displaystyle \scriptstyle h(x)\,}$ A distance function of a convex or star body[6] ● Height[24]
${\displaystyle I\,}$ ${\displaystyle \scriptstyle \Im (z)\,}$ Imaginary part of a complex number

${\displaystyle \scriptstyle I_{n}\,}$ Identity matrix of order ${\displaystyle \scriptstyle n\,}$[25]
${\displaystyle \scriptstyle \mathbb {I} \,}$ Imaginary numbers
${\displaystyle \scriptstyle \mathbb {I} \,}$ Integers (more commonly ${\displaystyle \scriptstyle \mathbb {Z} \,}$)[3]

${\displaystyle i\,}$ ● The imaginary unit ${\displaystyle \scriptstyle {\sqrt {-1}}\,}$[6]

● An iterator variable
● An integer[6]

${\displaystyle J\,}$
${\displaystyle j\,}$ ● Alternative symbol for the imaginary unit ${\displaystyle \scriptstyle {\sqrt {-1}}\,}$in most electrical engineering applications.[26]

● An iterator variable, related in some way to ${\displaystyle \scriptstyle i\,}$
● An integer[6]

${\displaystyle K\,}$
${\displaystyle k\,}$ ${\displaystyle \scriptstyle k(m)\,}$ Squarefree kernel of ${\displaystyle \scriptstyle m\,}$[27] ● An integer[6]
${\displaystyle L\,}$ Linnik's constant[28] ${\displaystyle \scriptstyle L_{n}\,}$ The ${\displaystyle \scriptstyle n\,}$th Lucas number[29]
${\displaystyle l\,}$ ● An integer[6]
${\displaystyle M\,}$

${\displaystyle \scriptstyle M(n)\,}$ Mertens function
${\displaystyle \scriptstyle M_{n}\,}$ Mersenne number ${\displaystyle \scriptstyle 2^{n}-1\,}$[30]

${\displaystyle m\,}$ ● An integer related in some way to ${\displaystyle \scriptstyle n\,}$
${\displaystyle N\,}$

${\displaystyle \scriptstyle \mathbb {N} \,}$ The set of natural numbers, including 0[31], though sometimes also used to mean the same thing but excluding 0.[15]
${\displaystyle \scriptstyle \mathbb {N} _{0}\,}$ The set of natural numbers, including 0[15]
${\displaystyle \scriptstyle \mathbb {N} ^{*}\,}$ The set of natural numbers, excluding 0.
${\displaystyle \scriptstyle \mathbb {N} (x)\,}$ Norm of ${\displaystyle \scriptstyle x\,\in \,\mathbb {Q} ({\sqrt {m}})\,}$[32]

${\displaystyle n\,}$ ● An integer
${\displaystyle O\,}$

${\displaystyle \scriptstyle O(\cdot )\,}$ A Landau symbol[33]
${\displaystyle \scriptstyle \mathbb {O} \,}$ Octonions[3]

${\displaystyle o\,}$

● The origin[6]
${\displaystyle \scriptstyle o(\cdot )\,}$ A Landau symbol[34]

${\displaystyle P\,}$

${\displaystyle \scriptstyle \mathbb {P} \,}$ The set of all rational primes[35]
${\displaystyle \scriptstyle \mathbb {P} ^{n}\,}$ ${\displaystyle \scriptstyle n\,}$-dimensional real projective space[3]

${\displaystyle p\,}$

${\displaystyle \scriptstyle p_{n}\,}$ The ${\displaystyle \scriptstyle n\,}$th prime number
${\displaystyle \scriptstyle p_{n}\,}$ The ${\displaystyle \scriptstyle n\,}$th partition number ("always identified as such")[36]

● An arbirtrary prime number (sometimes specified to be odd)
${\displaystyle Q\,}$

${\displaystyle \scriptstyle \mathbb {Q} \,}$ The set of rational numbers[37]
${\displaystyle \scriptstyle \mathbb {Q} ^{*}\,}$ The set of rational numbers, excluding 0.
${\displaystyle \scriptstyle \mathbb {Q} (m)\,}$ Least field containing ${\displaystyle \scriptstyle \mathbb {Q} \,}$ and ${\displaystyle \scriptstyle {\sqrt {m}}\,}$[32]

${\displaystyle q\,}$

● A prime number bearing some relation to ${\displaystyle \scriptstyle p\,}$
● A power of a prime[38]

${\displaystyle R\,}$ ${\displaystyle \scriptstyle \Re (z)\,}$ Real part of a complex number ${\displaystyle \scriptstyle R_{n}\,}$ Repunit (base ${\displaystyle \scriptstyle b\,}$), ${\displaystyle \scriptstyle {\frac {b^{n-1}-1}{b-1}}\,}$[39]

${\displaystyle \scriptstyle \mathbb {R} \,}$ The set of real numbers[40]
${\displaystyle \scriptstyle \mathbb {R} ^{*}\,}$ The set of real numbers, excluding 0.
${\displaystyle \scriptstyle \mathbb {R} ^{n}\,}$ ${\displaystyle \scriptstyle n\,}$-dimensional Euclidean space[6]
${\displaystyle \scriptstyle \mathbb {R} P^{n}\,}$ ${\displaystyle \scriptstyle n\,}$-dimensional projective space[3]
${\displaystyle \scriptstyle \mathbb {R} *\,}$ Nonzero elements of the ring ${\displaystyle \scriptstyle \mathbb {R} \,}$[32]
${\displaystyle \scriptstyle \mathbb {R} (x)\,}$ Ring of polynomials with coefficients in ${\displaystyle \scriptstyle \mathbb {R} \,}$[32]

${\displaystyle r\,}$

● An iterator (especially in French texts)
● An integer[6]

${\displaystyle S\,}$ Schnirelman's constant[41] ${\displaystyle \scriptstyle \mathbb {S} ^{n}\,}$ ${\displaystyle \scriptstyle n\,}$-sphere[3]
${\displaystyle s\,}$
${\displaystyle T\,}$ ${\displaystyle \scriptstyle T_{n}\,}$ The ${\displaystyle \scriptstyle n\,}$th triangular number ${\displaystyle \scriptstyle \mathbb {T} ^{n}\,}$ ${\displaystyle \scriptstyle n\,}$-torus[3]
${\displaystyle t\,}$

● Time[43]
● An integer[6]
${\displaystyle \scriptstyle it\,}$ Imaginary part of a complex number, by Riemann's notation[44]

${\displaystyle U\,}$
${\displaystyle u\,}$ ● A point in a Euclidean space ${\displaystyle \scriptstyle \mathbb {R} ^{n}\,}$[6]
${\displaystyle V\,}$ Volume of a 3-dimensional solid
${\displaystyle v\,}$ ● A point in a Euclidean space ${\displaystyle \scriptstyle \mathbb {R} ^{n}\,}$[6]
${\displaystyle W\,}$ ${\displaystyle \scriptstyle \mathbb {W} \,}$ The set of whole numbers, excluding 0[45]
${\displaystyle w\,}$ ● A point in a Euclidean space ${\displaystyle \scriptstyle \mathbb {R} ^{n}\,}$[6]
${\displaystyle X\,}$
${\displaystyle x\,}$

● A real number
● A point on the horizontal axis of the Cartesian 2- or 3-dimensional space
● A point in a Euclidean space ${\displaystyle \scriptstyle \mathbb {R} ^{n}\,}$[6]

${\displaystyle Y\,}$
${\displaystyle y\,}$

● A point on the vertical axis of the Cartesian 2- or 3-dimensional space
● A point in a Euclidean space ${\displaystyle \scriptstyle \mathbb {R} ^{n}\,}$[6]

${\displaystyle Z\,}$

${\displaystyle \scriptstyle \mathbb {Z} \,}$ Set of rational integers[45] (from German "die Zahlen," meaning "the numbers")
${\displaystyle \scriptstyle \mathbb {Z} ^{*}\,}$ The set of integers, excluding 0.
${\displaystyle \scriptstyle \mathbb {Z} ^{-}\,}$ Set of negative integers
${\displaystyle \scriptstyle \mathbb {Z} ^{+}\,}$ Set of positive integers (also ${\displaystyle \scriptstyle \mathbb {N} \,}$)[46]
${\displaystyle \scriptstyle \mathbb {Z} _{n}\,}$ Ring of integers ${\displaystyle \scriptstyle {\pmod {n}}\,}$[32]

${\displaystyle z\,}$

● A point on the depth axis of the 3-dimensional Cartesian space
● A point in a Euclidean space ${\displaystyle \scriptstyle \mathbb {R} ^{n}\,}$[6]

${\displaystyle \scriptstyle {\overline {z}}\,}$ Complex conjugate[15]
${\displaystyle \scriptstyle |z|\,}$ Modulus, absolute value[15]

Also, the letters A to Z are used as digits meaning 10 to 35 in bases 11 to 36. The vast majority of computer programming texts use uppercase letters for this purpose; however, Mathematica uses lowercase letters.

## Notes

1. Such as in P. M. Gruber & C. G. Lekkerkerker, Geometry of Numbers 2nd Ed. North-Holland Mathematical Library series, Volume 37 Amsterdam: North-Holland (1987)
2. N. J. A. Sloane & Simon Plouffe, The Encyclopedia of Integer Sequences. San Diego: Academic Press (1995): p. xi
3. Weisstein, Eric W. "Doublestruck." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Doublestruck.html
4. Ethan D. Bolker, Elementary Number Theory: An Algebraic Approach Mineola, New York: Dover Publications (1969, reprinted 2007): 174
5. N. J. A. Sloane & Simon Plouffe, The Encyclopedia of Integer Sequences. San Diego: Academic Press (1995): p. xi
6. P. M. Gruber & C. G. Lekkerkerker, Geometry of Numbers 2nd Ed. North-Holland Mathematical Library series, Volume 37 Amsterdam: North-Holland (1987): 1
7. Robert Oman & Daniel Oman, Calculus for the Utterly Confused. New York: McGraw-Hill (2007): 254
8. Paulo Ribenboim. The New Book of Prime Number Records New York: Springer (1996) p. xxi
9. Paulo Ribenboim. The New Book of Prime Number Records New York: Springer (1996) p. xx
10. Peter Kotelenez, Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic Equations. New York: Springer (2008): 439
11. Robert Oman & Daniel Oman, Calculus for the Utterly Confused. New York: McGraw-Hill (2007) p. 254
12. N. J. A. Sloane & Simon Plouffe, The Encyclopedia of Integer Sequences. San Diego: Academic Press (1995): p. xi
13. N. J. A. Sloane & Simon Plouffe, The Encyclopedia of Integer Sequences. San Diego: Academic Press (1995): p. xi. More usually rendered as ${\displaystyle \scriptstyle {\binom {n}{k}}\,}$ when not constrained to typewriter conventions.
14. Steven J. Miller & Ramin Takloo-Bighash An Invitation to Modern Number Theory (2006) Princeton and Oxford: Princeton University Press, p. xix
15. Eberhard Freitag & Rolf Busam, Complex Analysis, 2nd Ed. (2009) Springer-Verlag (Universitext), pp. 519-520.
16. J. W. S. Cassels, An Introduction to the Geometry of Numbers. Berlin: Springer-Verlag (1997) p. VIII
17. Manfred R. Schroeder, Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing and Self-Similarity 5th Ed. Springer (2009) p. 405
18. Manfred R. Schroeder, Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing and Self-Similarity 5th Ed. Springer (2009) p. 405
19. Thomas Koshy, Elementary Number Theory with Applications. Harcourt Academic Press (2002): p. 122
20. Paulo Ribenboim. The New Book of Prime Number Records New York: Springer (1996) p. xvii
21. Steven J. Miller & Ramin Takloo-Bighash An Invitation to Modern Number Theory (2006) Princeton and Oxford: Princeton University Press, p. xix
22. Thomas Koshy, Elementary Number Theory with Applications. Harcourt Academic Press (2002): p. 131. Hardly an established convention. ${\displaystyle F_{n}\,}$ is more frequently used, even in texts that also reference Fibonacci numbers.
23. Paulo Ribenboim. The New Book of Prime Number Records New York: Springer (1996) p. xix
24. Robert Oman & Daniel Oman, Calculus for the Utterly Confused. New York: McGraw-Hill (2007) p. 254
25. Thomas Koshy, Elementary Number Theory with Applications. Harcourt Academic Press (2002): p. 128
26. Paul J. Nahin, An Imaginary Tale: The Story of ${\displaystyle \scriptstyle {\sqrt {-1}}\,}$. Princeton, New Jersey: Princeton University Press (1988): 125
27. Paulo Ribenboim. The New Book of Prime Number Records New York: Springer (1996) p. xviii
28. Paulo Ribenboim. The New Book of Prime Number Records New York: Springer (1996) p. xxi
29. Thomas Koshy, Elementary Number Theory with Applications. Harcourt Academic Press (2002): p. 129
30. Thomas Koshy, Elementary Number Theory with Applications. Harcourt Academic Press (2002): p. 369
31. Steven J. Miller & Ramin Takloo-Bighash, An Invitation to Modern Number Theory, (2006) Princeton and Oxford: Princeton University Press, p. xix.
32. Ethan D. Bolker, Elementary Number Theory: An Algebraic Approach Mineola, New York: Dover Publications (1969, reprinted 2007): 175
33. Somewhat of a misnomer, but too ingrained to be changed now. Władysław Narkiewicz, The Development of Prime Number Theory: From Euclid to Hardy and Littlewood Berlin: Springer-Verlag (2000): p. xi
34. Somewhat of a misnomer, but too ingrained to be changed now. Władysław Narkiewicz, The Development of Prime Number Theory: From Euclid to Hardy and Littlewood Berlin: Springer-Verlag (2000): p. xi
35. Władysław Narkiewicz, The Development of Prime Number Theory: From Euclid to Hardy and Littlewood Berlin: Springer-Verlag (2000): p. xi
36. N. J. A. Sloane & Simon Plouffe, The Encyclopedia of Integer Sequences. San Diego: Academic Press (1995): p. xii
37. Steven J. Miller & Ramin Takloo-Bighash An Invitation to Modern Number Theory (2006) Princeton and Oxford: Princeton University Press, p. xix
38. N. J. A. Sloane & Simon Plouffe, The Encyclopedia of Integer Sequences. San Diego: Academic Press (1995): p. xii
39. Thomas Koshy, Elementary Number Theory with Applications. Harcourt Academic Press (2002): p. 104
40. Steven J. Miller & Ramin Takloo-Bighash An Invitation to Modern Number Theory (2006) Princeton and Oxford: Princeton University Press, p. xix
41. Paulo Ribenboim. The New Book of Prime Number Records New York: Springer (1996) p. xxii
42. Władysław Narkiewicz, The Development of Prime Number Theory: From Euclid to Hardy and Littlewood Berlin: Springer-Verlag (2000): p. xi
43. Dale Johnson, Teach Yourself Visually: Calculus Hoboken, New Jersey: Wiley (2008): p. 139
44. Władysław Narkiewicz, The Development of Prime Number Theory: From Euclid to Hardy and Littlewood Berlin: Springer-Verlag (2000): p. xi
45. Steven J. Miller & Ramin Takloo-Bighash An Invitation to Modern Number Theory (2006) Princeton and Oxford: Princeton University Press, p. xix.
46. Thomas Koshy, Elementary Number Theory with Applications. Harcourt Academic Press (2002): p. 3