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