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Holt Algebra 2
1-1 Sets of Numbers
Warm UpOrder from least to greatest.
1. 10, –5, –10, 0, 5
2.
–10, –5, 0, 5, 10
3.2 ,7652.2 ,2
11 ,5 ,
,. ,. , , 765223252
11
Holt Algebra 2
1-1 Sets of Numbers
Rational NumbersRatios 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.
IntegersNatural numbers, their negatives, and zero.. . . , −3, −2, −1, 0, 1, 2, 3, . . .
Whole NumberNon-negative integers.0, 1, 2, 3, . . .
Natural numbersCounting numbers.1, 2, 3, 4, . . .
Irrational NumbersCannot be written as a fraction. The decimal form is non-terminating and non-repeating.
3.031 ,17.0
10017
,146
46 ,73
,21
,5 ,3
Real Numbers
Holt Algebra 2
1-1 Sets of NumbersClassifying Numbers
211 QR,
5 irrationalR,
3.2 QR,
7652.2 QR,
irrationalR,
7 ZQR ,,
0 WZQR ,,,
17 NWZQR ,,,,
Holt Algebra 2
1-1 Sets of Numbers
Real Numbers
Rational Numbers Irrational Numbers
Integers
Whole Numbers
Natural Numbers
Holt Algebra 2
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 striped-billiard-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.”
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.”
Helpful Hint
Holt Algebra 2
1-1 Sets of Numbers
Roster Notation Lists each element of a set in braces. The set of striped-billiard-ball 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.
)0,3(
Holt Algebra 2
1-1 Sets of Numbers
]8,2(
Express the interval in set notation and then graph.
Holt Algebra 2
1-1 Sets of Numbers
)8,2[
Express the interval in set notation and then graph.
Holt Algebra 2
1-1 Sets of Numbers
]4,6[
Express the interval in set notation and then graph.
Holt Algebra 2
1-1 Sets of Numbers
),2[
Express the interval in set notation and then graph.
Holt Algebra 2
1-1 Sets of Numbers
}8|{ xx
Express the set in interval notation and then graph.
Holt Algebra 2
1-1 Sets of Numbers
}64|{ xx
Express the set in interval notation and then graph.
Holt Algebra 2
1-1 Sets of Numbers
}72|{ xx
Express the set in interval notation and then graph.
Holt Algebra 2
1-1 Sets of Numbers
}3|{ xx
Express the set in interval notation and then graph.
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:
)irrational(R 6
(RQZWN), 4
,(RQ)81
(RQ), 6.897-
(RQZ), 4
100 - 3.)
)(12, [8,12]; (0,8); .)42
1614|
;1312| ;1211|.)41
3,4,5,-1,0,1,2,5,-4,-3,-2- 11.)
5 of mulitples negativenon 10.)
3x-5|x 9.)
) (30,or 20) [1, 7.)
5)- ,(- 6.)
10] (-10, 5.)
xx
xxxx
Holt Algebra 2
1-1 Sets of Numbers
Holt Algebra 2
1-1 Sets of Numbers
Review, Classifying NumbersPut in order from least to greatest, then classify:
27
QR,
9
27
- ,125. 1,- 6, ,2 ,9- 1.5,
QR,
2
, irrationalRQR,
1
ZQR ,,
125.5.1
ZQR ,,
6
NWZQR ,,,,
Holt Algebra 2
1-1 Sets of Numbers
Review, Roster, Set, and Interval NotationMost women have shoe sizes ranging in half sizes from 5 to 11. Represent this on a number lines and in roster notation.
,11,10,10,9,9,8,8,7,7,6,65,5 21
21
21
21
21
21
Holt Algebra 2
1-1 Sets of Numbers
Review, Roster, Set, and Interval NotationChildren 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.
215| :Set
]21 ,5[:Interval
xx
5 21