Set Notation
Name:
We’ve learned about sets. Let’s learn some different ways to express
sets. First, let’s remember some symbols that have to do with sets.
 -an element of
{ } or Ø -empty set
 or
Z or
1)
 -not an element of
subset
means real numbers
means integers
Roster notation - This is a list of the elements in a set.
The set of integers from 2 to 6, inclusive.
The set of positive integers.
Represent the following using roster notation.
1. All positive even integers.
2. All odd integers between 17 and 27,
inclusive.
3. All integers between -5 and 5,
inclusive.
4.
{0,1,2,3,4,5,6,7,8,9}
5.
{-1,-3,-5,-7,…}
We can also describe certain sets using another type of notation called “set-builder notation.”
2) Set-builder notation - To use set builder notation, we use some of our symbols. Look at these examples and
see if you get the hang of it!
This means, “the set of integers from 2 to 6, inclusive.”
The statement is read, "All x that are elements of the set of
integers such that x is between 2 and 6 inclusive."
The statement is read, "All x that are elements of the set of
integers such that the x values are greater than 0."
It is also possible to use a colon ( : ), instead of the | , to represent the words "such that".
is the same as
Represent the following sets using set-builder notation:
6. All negative integers.
7. All integers between 17 and 27,
inclusive.
8. All real numbers greater than
-5 and less than or equal to 5.
9.
{x  Z | x  5}
10.
{x  R | 0  x  10}
3) Interval notation is another way to represent these sets. We need to learn two new symbols.
When using interval notation, the symbol:
(
means “not included” or “open”.
[
means “included” or “closed”.
as an
inequality.
in interval
notation.
 means “and”
 means “or”
Let’s do a few in interval notation.
11. All real numbers between 17 and 27, inclusive.
12. All real numbers greater than
-5 and less than or equal to 5.
13.
0,9
14.
 6,1
4) You can also represent sets by graphing on a number line
Interval Notation: (description)
Open Interval:
Closed Interval
(number line graph)
Half-Open Interval:
Half-Open Interval:
Non-ending Interval:
Non-ending Interval:
Complete the table:
Set-builder
Notation
1.
{x   | x  2}
2.
{x   | x  3}
Interval Notation
3.
 2,4
4.
( , 4)
5.
Graph
{x  Z | x  14}
6.
Word Description
Roster
Set-Builder Notation
7. Integers greater than 4
8.
{x  Z | 1  x  5}