# 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.)