1-1 Sets of Numbers
Warm Up
Order from least to greatest.
1. 10, –5, –10, 0, 5
–10, –5, 0, 5, 10
2.  , 5,  11 , 2.7652, 2.3
2
11

, 5, 2.3, 2.7652, 
2
Holt Algebra 2
1-1 Sets of Numbers
Real Numbers
Rational Numbers
Ratios of integers, written in the form r=m/n, where m and n are integers and n≠0.
The decimal form either terminates or repeats.

1 3
46 17
1
, , 46 
,
 0.17,  0.3
2 7
1 100
3
Integers
Natural numbers, their negatives, and zero.
. . . , −3, −2, −1, 0, 1, 2, 3, . . .
Whole Number
Non-negative integers.
0, 1, 2, 3, . . .
Natural numbers
Counting numbers.
1, 2, 3, 4, . . .
Irrational Numbers
Cannot be written as a fraction.
The decimal form is non-terminating and non-repeating.
3, 5, 
Holt Algebra 2
1-1 Sets of Numbers
Classifying Numbers

11
2
R, Q
5
R, irrational
2.3
2.7652

Holt Algebra 2
R, Q
R, Q
R, irrational
7
0
R, Q, Z
R, Q, Z , W
17 R, Q, Z , W , N
1-1 Sets of Numbers
Real Numbers
Rational Numbers
Integers
Whole Numbers
Natural Numbers
Holt Algebra 2
Irrational Numbers
1-1 Sets of Numbers
Holt Algebra 2
1-1 Sets of Numbers
Set-Builder Notation
Uses the properties of the elements in the set to define the set. Inequalities and the
element symbol  are often used in the set-builder notation. The set of stripedbilliard-ball numbers, or {9, 10, 11, 12, 13, 14, 15}, is represented in set-builder
notation below:
The set of all numbers x such that x has the given properties
{x | 8 < x ≤ 15 and x  N}
Read the above as “the set of all numbers x such that x is greater than 8 and less
than or equal to 15 and x is a natural number.”
Helpful Hint
The symbol  means “is an element of.” So x  N is read “x is an element of the set
of natural numbers,” or “x is a natural number.”
Holt Algebra 2
1-1 Sets of Numbers
Roster Notation
Lists each element of a set in braces. The set of striped-billiardball numbers is written {9, 10, 11, 12, 13, 14, 15}. This
notation can be used for finite sets. Cannot use roster notation
for infinite sets.
Interval Notation
Uses the symbols [and] to include endpoints and (and) to
exclude endpoints from an interval.
Holt Algebra 2
1-1 Sets of Numbers
Holt Algebra 2
1-1 Sets of Numbers
Because ∞ and –∞ are not numbers, they cannot be included
in a set of numbers, so parentheses are used to enclose them
in an interval. The table shows the relationship among some
methods of representing intervals.
Holt Algebra 2
1-1 Sets of Numbers
Some representations of the same sets of real
numbers are shown.
Holt Algebra 2
1-1 Sets of Numbers
Is there a difference between saying that a real number is
positive and saying that a real number is nonnegative?
Holt Algebra 2
1-1 Sets of Numbers
Interval/Set Notation and Number Line Graphs
Holt Algebra 2
1-1 Sets of Numbers
Express the
interval in set
notation and
then graph.
(3,0)
Holt Algebra 2
1-1 Sets of Numbers
Express the
interval in set
notation and
then graph.
(2,8]
Holt Algebra 2
1-1 Sets of Numbers
Express the
interval in set
notation and
then graph.
[2,8)
Holt Algebra 2
1-1 Sets of Numbers
Express the
interval in set
notation and
then graph.
[6,4]
Holt Algebra 2
1-1 Sets of Numbers
Express the
interval in set
notation and
then graph.
[2, )
Holt Algebra 2
1-1 Sets of Numbers
Express the set
in interval
notation and
then graph.
{x | x  8}
Holt Algebra 2
1-1 Sets of Numbers
Express the set
in interval
notation and
then graph.
{x | 4  x  6}
Holt Algebra 2
1-1 Sets of Numbers
Express the set
in interval
notation and
then graph.
{x | 2  x  7}
Holt Algebra 2
1-1 Sets of Numbers
Express the set
in interval
notation and
then graph.
{x | x  3}
Holt Algebra 2
1-1 Sets of Numbers
Express the graph
in set and interval
notation.
Holt Algebra 2
1-1 Sets of Numbers
Express the graph
in set and interval
notation.
Holt Algebra 2
1-1 Sets of Numbers
Express the graph
in set and interval
notation.
Holt Algebra 2
1-1 Sets of Numbers
Express the graph
in set and interval
notation.
Holt Algebra 2
1-1 Sets of Numbers
Express the graph
in set and interval
notation.
Holt Algebra 2
1-1 Sets of Numbers
Express the graph
in set and interval
notation.
Holt Algebra 2
1-1 Sets of Numbers
Answers to Homework, page 10:
100
(RQZ),
4
- 6.897 (RQ),
5.) (-10, 10]
6.) (-, - 5)
1
(RQ),
8
4 (RQZWN),
9.) x | -5  x  3
3.) -
6 (R irrational)
7.) [1, 20) or (30, )
10.) non  negative mulitples of 5
11.) - 5,-4,-3,-2,-1,0,1,2,3,4,5
41.)x | 11  x  12; x | 12  x  13;
x | 14  x  16
42.) (0,8); [8,12]; (12, )
Holt Algebra 2
1-1 Sets of Numbers
Holt Algebra 2
1-1 Sets of Numbers
Review, Classifying Numbers
Put in order from least to greatest, then classify:
 1.5,
7

2
R, Q
Holt Algebra 2
- 9,
2 ,
 9
 1.5
R, Q, Z
6,
- 1,
5.12,
7
2
6
2
5.12
R, Q
R, irrational
R, Q
R, Q, Z
R, Q, Z , W , N
1
1-1 Sets of Numbers
Review, Roster, Set, and Interval
Notation
Most women have shoe sizes ranging in half sizes from 5 to 11.
Represent this on a number lines and in roster notation.
5,5
Holt Algebra 2
1
2
,6,6 ,7,7 ,8,8 ,9,9 ,10,10 ,11
1
2
1
2
1
2
1
2
1
2
1-1 Sets of Numbers
Review, Roster, Set, and Interval
Notation
Children must be 5 to enter school and must leave once they
turn 21. Represent this on a number line and using interval and
set notation.
Holt Algebra 2
5
21
Interval :
Set :
[5, 21]
x | 5  x  21