Commonly used letters

This table describes how to type commonly used letters, along with usage examples (including the typeset equivalent.) If the expression you need is not listed, please define your own and explain the meaning of your notation.

Expression Description Examples

$\displaystyle x$

A variable, or unknown. The letter x is used most commonly for an unknown, although there are a few conventions, as follows, for other letters. Try to use only lowercase letters for variables wherever possible. Uppercase letters are many times used for matrices, sets, and other things. Let be the number of tickets sold for the event...

Let x be the number of tickets sold for the event...

$\displaystyle x,y$

Real numbers. Let and be any two real numbers...

Let x and y be any two real numbers...

$\displaystyle \mathbf{u,v}$

Vectors. For vectors $\mathbf{u}=\langle a,b \rangle$ and $\mathbf{v}=\langle c,d \rangle \ldots$

For vectors u = <a,b> and v = <c,d>...

$\displaystyle n$

Natural number. If true for n, prove true for n+1...

$\displaystyle q,r$

Rational numbers. For all rational numbers q and r...

$\displaystyle i$

The imaginary unit , where . i^2 = -1

$\displaystyle z$

Complex number. Let z be a complex number of the form x + iy...

$\displaystyle f,g,h$

Functions. Let be a function defined by

Let f be a function defined by f(x) = x^3.

$\displaystyle e$

The constant , the base of the natural logarithm.

$\displaystyle \ln{x}=\log_{e}x$

ln(x) = log_e (x)

Lowercase Greek letters In most cases, the intended ``case'' of a Greek letter can be inferred from the context.

$\displaystyle \alpha, \beta, \gamma, \delta, \epsilon, \theta, etc.$

alpha, beta, gamma, delta, epsilon, theta, etc.

Uppercase Greek letters To explicitly indicate the uppercase, type the first letter in uppercase.

$\displaystyle \Gamma, \Delta, \Theta, \Lambda, \Xi, \Pi, \Sigma, etc.$

Gamma, Delta, Theta, Lambda, Xi, Pi, Sigma, etc.

Expression	Description	Examples
$\displaystyle x$	A variable, or unknown. The letter x is used most commonly for an unknown, although there are a few conventions, as follows, for other letters. Try to use only lowercase letters for variables wherever possible. Uppercase letters are many times used for matrices, sets, and other things.	Let be the number of tickets sold for the event... Let x be the number of tickets sold for the event...
$\displaystyle x,y$	Real numbers.	Let and be any two real numbers... Let x and y be any two real numbers...
$\displaystyle \mathbf{u,v}$	Vectors.	For vectors $\mathbf{u}=\langle a,b \rangle$ and $\mathbf{v}=\langle c,d \rangle \ldots$ For vectors u = <a,b> and v = <c,d>...
$\displaystyle n$	Natural number.	If true for n, prove true for n+1...
$\displaystyle q,r$	Rational numbers.	For all rational numbers q and r...
$\displaystyle i$	The imaginary unit , where .	i^2 = -1
$\displaystyle z$	Complex number.	Let z be a complex number of the form x + iy...
$\displaystyle f,g,h$	Functions.	Let be a function defined by Let f be a function defined by f(x) = x^3.
$\displaystyle e$	The constant , the base of the natural logarithm.	$\displaystyle \ln{x}=\log_{e}x$ ln(x) = log_e (x)
Lowercase Greek letters	In most cases, the intended ``case'' of a Greek letter can be inferred from the context.	$\displaystyle \alpha, \beta, \gamma, \delta, \epsilon, \theta, etc.$ alpha, beta, gamma, delta, epsilon, theta, etc.
Uppercase Greek letters	To explicitly indicate the uppercase, type the first letter in uppercase.	$\displaystyle \Gamma, \Delta, \Theta, \Lambda, \Xi, \Pi, \Sigma, etc.$ Gamma, Delta, Theta, Lambda, Xi, Pi, Sigma, etc.