# 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

Question: What is the best variable to represent a number, with universal set $\mathbb{R}\,$?
Choices: $\,x\,$, $\,j\,$, or $\,S$
Answer: $x$
Question: What is the best variable to represent a member of the set $\,[-1,3)\,$?
Choices: $\,B\,$, $\,k\,$, or $\,t$
(You may want to review interval notation.)
Answer: $t$
Question: What is the best variable to represent a set ?
Choices: $\,t\,$, $\,A\,$, or $\,m$
Answer: $A$
Question: What is the best variable to represent a member of the set $\{3,4,5,\ldots\}\,$?
Choices: $\,k\,$, $\,S\,$, or $\,y$
(You may want to review list notation.)
Answer: $k$