# Using Mathematical Conventions

Want some basic practice with variables first? Introduction to Variables

Recall:

$\mathbb{R}\,$ is the set of real numbers: $\mathbb{R} = (-\infty,\infty)$

$\mathbb{Z}\,$ is the set of integers: $\mathbb{Z} = \{\ldots,-3,-2,-1,0,1,2,3,\ldots\}$

*Numbers* are usually represented by lowercase letters, like
$\,a\,$, $\,n\,$, or $\,x\,$.

*Sets* are usually represented by uppercase letters, like
$\,A\,$, $\,B\,$, or $\,S\,$.

A variable with universal set
$\mathbb{R}\,$
(or, any *interval* of real numbers)
is most likely to be named with a lowercase
letter from the *end* of the alphabet;
particularly $\,t\,$, $\,x\,$, or $\,y\,$.

A variable with universal set
$\mathbb{Z}\,$
(or, any *subset* of the integers)
is most likely to be named with a lowercase letter
near the *middle* of the alphabet;
particularly $\,i\,$, $\,j\,$, $\,k\,$, $\,m\,$, or $\,n\,$.

## Examples

Choices: $\,x\,$, $\,j\,$, or $\,S$

Choices: $\,B\,$, $\,k\,$, or $\,t$

(You may want to review interval notation.)

*set*?

Choices: $\,t\,$, $\,A\,$, or $\,m$

Choices: $\,k\,$, $\,S\,$, or $\,y$

(You may want to review list notation.)