Using Mathematical Conventions

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

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