USING MATHEMATICAL CONVENTIONS
• PRACTICE (online exercises and printable worksheets)
• This page gives an in-a-nutshell discussion of the concepts.
For a complete discussion, read the text (and solutions are here).
• 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: $k$
Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
‘Undoing’ a Sequence of Operations

What is the best variable to represent $\ldots$

 (MAX is 13; there are 13 different problem types)