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# Roman letters used in mathematics

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 Title: Roman letters used in mathematics Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Roman letters used in mathematics

Many letters of the Latin alphabet, both capital and small, are used in mathematics, science and engineering to denote by convention specific or abstracted constants, variables of a certain type, units, multipliers, physical entities. Certain letters, when combined with special formatting, take on special meaning.

Below is an alphabetical list of the letters of the alphabet with some of their uses. The field in which the convention applies is mathematics unless otherwise noted.

## Bb

• B represents:
• the digit "11" in hexadecimal and other positional numeral systems with a radix of 12 or greater
• the second corner of a triangle
• a ball (also denoted by ℬ (\mathcal{B}) or 𝔹 (\mathbb{B}))
• a basis of a vector space or of a filter (both also denoted by ℬ (\mathcal{B}))
• in econometrics and time-series statistics it is often used for the (back)lag operator, the formal parameter of the lag polynomial
• B with various subscripts represents several variations of Brun's constant and Betti numbers
• b represents:

## Cc

• C represents:
• the third corner of a triangle
• the digit "12" in hexadecimal and other positional numeral systems with a radix of 13 or greater
• the unit coulomb of electrical charge
• capacitance in electrical theory
• with indices denotes the number of combinations, a binomial coefficient
• together with a degree symbol (°) represents the Celsius measurement of temperature = °C
• ℂ (\mathbb{C}) represents the set of complex numbers
• A vertically elongated C with an integer subscript n sometimes denotes the n-th coefficient of a formal power series.
• c represents:
• c represents:
• the speed of light in vacuum
• the third side of a triangle (opposite corner C)
• Small bold C denotes the cardinality of the set of real numbers (the "continuum"), or, equivalently, of the power set of natural numbers

## Dd

• D represents the digit "13" in hexadecimal and other positional numeral systems with a radix of 14 or greater
• diffusion coefficient or diffusivity in dimensions of [length^2 / time]
• d represents
• the differential operator
• the unit day of time (86,400 s)
• the difference in an arithmetic sequence (e.g. Sn = n(2a+(n-1)d)/2)
• a metric operator/function

## Ee

• E represents:
• the digit "14" in hexadecimal and other positional numeral systems with a radix of 15 or greater
• an exponent in decimal numbers 1.2E3 is 1.2×10³ or 1200
• the set of edges in a graph or matroid
• the unit prefix exa (1018)
• Energy in physics
• Electric field denoted \boldsymbol{E}.
• Electromotive force, (denoted \mathcal{E} and measured in volts), refers to voltage.
• an event (as in P(E), which reads "the probability P of event E happening")
• e represents:
• Euler's number, a transcendental number equal to 2.71828182845... which is used as the base for natural logarithms
• a vector of unit length, especially in the direction of one of the coordinates axes
• the elementary charge in physics
• an electron, usually donated e- to distinguish against a positron e+
• the eccentricity of an ellipse

## Ii

• I represents:
• i represents:
• the imaginary unit, a complex number that is the square root of −1
• a subscript to denote the ith term (that is, a general term or index) in a sequence or list
• the index to the elements of a vector, written as a subscript after the vector name
• the index to the rows of a matrix, written as the first subscript after the matrix name
• an index of summation using the sigma notation
• the unit vector in Cartesian coordinates going in the X-direction, usual bold i

## Ll

• L represents:
• l represents:
• the unit of volume the litre
• the length of a side of a rectangle or a rectangular prism (e.g. V = lwh; A = lw)
• the last term of a sequence or series (e.g. Sn = n(a+l)/2)
• ℒ (\mathcal{L}) represents:

## Nn

• N represents
• NA represents the Avogadro constant which is the number of entities in one mole (used mainly in the counting of molecules and atoms) and is 6.022 141 79(30) × 10,23 mol −1
• ℕ (\mathbb{N}) represents the natural numbers
• n represents
• the number of columns in a matrix
• the "number of" in algebraic equations.
• A neutron, often shown as 10n
• the Number density of particles in a Volume
• the unit prefix nano (10−9)
• the nth term of a sequence or series (e.g. tn = a+(n-1)d)
• the principal quantum number

## Rr

• R represents:
• ℝ (\mathbb{R}) represents the set of real numbers and various algebraic structures built upon the set of real numbers, such as \mathbb{R}^n
• r represents:
• the radius of a circle or sphere
• the ratio of a geometric series (e.g. arn-1)
• the separation of two objects, for example in Coulomb's law

## Vv

• V represents:
• v represents the velocity in mechanics equations