list of overloaded symbols

list of overloaded symbols

By tradition, certain symbols in mathematics are

overloaded

with

multiple

meanings, often

resolvable

by

context

.

0.1

The Latin-1 alphabet

A

Hexadecimal

numeral 10. As

A

⁢

(

x

)

members of a

sequence

that are less than

x

function

a

First

variable

.

Real part

of

complex number

. As

a

⁢

(

n

)

sequence function (this is a frequent use in Sloane’s OEIS). As

a

n

, a

recurrence relation

, with

a

1

and

a

2

often assigned

literal

values.

B

Bernoulli number

. Hexadecimal numeral 11.

b

Second variable. Multiplied by an

imaginary unit

(usually

i

), the

imaginary part

of a complex number.

C

Roman numeral 100.

Catalan number

. Hexadecimal numeral 12. A fallback in the absence of

ℂ

, the set of complex numbers.

c

Third variable. A

constant

, ”not always the same!” (Finch, Guy). Complex number

c

=

a

+

b

⁢

i

. In physics, the constant of the speed of light.

D

Roman numeral 500. Hexadecimal numeral 13.

d

Divisor

. Digit.

Difference

.

E

Euler numbers

. The base of

natural logarithms

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 number

. 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 function

. Roman numeral 1000.

m

Arbitrary number related to

n

. In physics, a variable of matter.

P

Largest prime factor function. Number in the

Padovan sequence

.

Pell number

.

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

δ

S

, the silver ratio. As

δ

i

⁢

j

, or

δ

i

⁢

j

or

δ

j

i

, the

Kronecker delta

. As

δ

⁢

(

x

)

, the Dirac delta function.

Transition function

for a

Turing machine

.

ϵ

In

analysis

, an arbitrarily small value. The

trivial group

representation

, or sometimes the

identity element

in a group.

λ

Carmichael function

(sometimes

ψ

is used instead),

Liouville function

.

Π

Iterated

product

. 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 ratio

.

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

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