# Set builder notation

### Set builder notation

#### Lessons

A set is a collection of elements (usually numbers)

E.g. {$x \in R | x$ > 0} should be read as “the set of all x’s that are an element of the real numbers such that x is greater than 0.”

Special symbols:

- $R$ = real numbers

- $Z$ = integers

- $N$ = natural numbers

- $Q$ = rational numbers

- $C$ = complex numbers

- $I$ = imaginary numbers

• Introduction
Introduction to Set Builder Notation

i. What are sets?

ii. Why do we need set builder notations?

• 1.
Translating Intervals On Number Lines Into Set Builder Notation Form

Translate the following intervals into set builder notation form.

a)

b)

c)

d)

• 2.
Evaluating the Domains of Expressions in Set Builder Notation Form

What are the domains for the following expressions? Write the answers in set builder notation form.

a)
$\frac{1}{x}$

b)
$\sqrt x$

c)
$\frac{2}{x^{2} - 4}$