# list of overloaded symbols

## 0.1 The Latin-1 alphabet

$b$ 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 $\mathbb{C}$, 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.

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

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

$i$ Iterator. Imaginary unit.

$L$ Roman numeral 50. Liouville sum function.

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

$r$ Third prime. Remainder.

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

$y$ Second variable. Vertical axis label.

## 0.2 ASCII symbols

$\ast$ 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.

$\delta$ As $\delta_{S}$, the silver ratio. As $\delta_{ij}$, or $\delta^{ij}$ or $\delta^{i}_{j}$, the Kronecker delta. As $\delta(x)$, the Dirac delta function. Transition function for a Turing machine  .

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

$\Sigma$ Iterated sum. A set of symbols usable by a Turing machine.

Title list of overloaded symbols ListOfOverloadedSymbols 2013-03-22 16:41:55 2013-03-22 16:41:55 PrimeFan (13766) PrimeFan (13766) 11 PrimeFan (13766) Example msc 68N15 msc 00A99