list of overloaded symbols

By tradition, certain symbols in mathematics are overloaded with multipleMathworldPlanetmathPlanetmath meanings, often resolvable by context.

0.1 The Latin-1 alphabet

A Hexadecimal numeral 10. As A(x) members of a sequenceMathworldPlanetmath that are less than x functionMathworldPlanetmath

a First variable. Real partDlmfMathworldPlanetmath of complex numberMathworldPlanetmathPlanetmath. As a(n) sequence function (this is a frequent use in Sloane’s OEIS). As an, a recurrence relation, with a1 and a2 often assigned literalMathworldPlanetmath values.

B Bernoulli numberDlmfDlmfMathworldPlanetmathPlanetmath. Hexadecimal numeral 11.

b Second variable. Multiplied by an imaginary unitMathworldPlanetmath (usually i), the imaginary part of a complex number.

C Roman numeral 100. Catalan numberDlmfMathworldPlanetmath. Hexadecimal numeral 12. A fallback in the absence of , the set of complex numbers.

c Third variable. A constant, ”not always the same!” (Finch, Guy). Complex number c=a+bi. In physics, the constant of the speed of light.

D Roman numeral 500. Hexadecimal numeral 13.

d Divisor. Digit. DifferencePlanetmathPlanetmath.

E Euler numbersDlmfDlmfMathworldPlanetmathPlanetmath. The base of natural logarithmsMathworldPlanetmath in Mathematica’s InputForm. Hexadecimal numeral 14.

e The base of natural logarithms. Sylvester’s sequence. In physics, a variable of energy.

F Fermat number. Fibonacci numberDlmfMathworldPlanetmath. Hexadecimal numeral 15.

I Roman numeral 1. Imaginary unit in Mathematica’s InputForm.

i Iterator. Imaginary unit.

L Roman numeral 50. Liouville sum function.

M Mersenne number. Mertens functionMathworldPlanetmath. Roman numeral 1000.

m Arbitrary number related to n. In physics, a variable of matter.

P Largest prime factor function. Number in the Padovan sequenceMathworldPlanetmath. Pell numberMathworldPlanetmath. Perrin number.

r Third prime. Remainder.

x First variable. Horizontal axis label. Arbitrary real number.

y Second variable. Vertical axis label.

0.2 ASCII symbols

Convolution operator. Multiplication operator in most computer programming languages.

% Percentage symbol. Reference to previous output in Mathematica (probably a hidden reference to the musical bis repeat sign). Modulo operator in Basic, C, Java, Javascript, Perl, etc.

0.3 The Greek alphabet

If it seems that the entire Greek alphabet has been overloaded, this is actually not the case. Several uses have been proposed for the more popular letters, but there are other letters with few or no assigned uses. This is also the case of Greek letter that look almost the same as Latin-1 letters, so understandably these are not popular.

δ As δS, the silver ratio. As δij, or δij or δji, the Kronecker delta. As δ(x), the Dirac delta function. Transition function for a Turing machineMathworldPlanetmath.

ϵ In analysis, an arbitrarily small value. The trivial group representation, or sometimes the identity elementMathworldPlanetmath in a group.

λ Carmichael functionMathworldPlanetmath (sometimes ψ is used instead), Liouville functionDlmfMathworldPlanetmath.

Π Iterated productPlanetmathPlanetmath. A set of symbols usable by a Turing machine.

π Ratio of a circle’s radius to its circumference. Prime counting function. Totient function in Euler’s notebooks.

Σ Iterated sum. A set of symbols usable by a Turing machine.

ϕ Totient function. Golden ratioMathworldPlanetmath.

Title list of overloaded symbols
Canonical name ListOfOverloadedSymbols
Date of creation 2013-03-22 16:41:55
Last modified on 2013-03-22 16:41:55
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 11
Author PrimeFan (13766)
Entry type Example
Classification msc 68N15
Classification msc 00A99