MATH 102 – Beginning Algebra I
Classifying Real Numbers – Section 1.1

1.  Use the following definitions of subsets of real numbers.
	N = set of natural numbers = {1, 2, 3, 4, 5, . . .}
	W = set of whole numbers = { 0, 1, 2, 3, 4, 5, . . . }
	Z = set of integers = { . . . , -2, -1, 0, 1, 2, . . . }
Q = set of rational numbers = { | a and b are integers and b 0}.  Examples of rational numbers include
 (1) fractions, such as  
		 (2)  terminating decimals, such as  0.5 = 
		 (3) repeating decimals, such	
	 (4) all integers

I = set of irrational numbers = { x | x is a real number and x is not a rational number}. Examples are , , and  2.96451256 . . . (non-repeating, non-terminating decimals)

R= set of real numbers = the set of all rational numbers, together with all irrational numbers

2.	Name every set to which the following real numbers belong.

	-2			12.21	-	11	.713713...	
irrational								
rational								
integer								
whole								

3.	Listing elements of a set is called writing a roster.  Use the roster method to write each given set.

a.	{w | w is a whole number and w is less than 7}

b.	{ I  | I  is an integer and I is between -3 and 3 inclusive}

c.	{x | x is a whole number and 0 < x < 1}

d.	{t | t is a natural number and 7 < t < 14}

4.	Determine if the statement is true or false.  If the statement is false, explain why it is false, and correct it so that it is true.

a.	Every integer is also a whole number.

b.	Every integer is a rational number.

c.	Every rational number is also an irrational number.
										
d.	Every whole number is also an integer.

e.	Every natural number is also a whole number.

f.	Every nonterminating decimal repeats.

g.	The number  is a rational number but  is not.

h.	The number 0 is a whole number but not an integer.

5.	Explain the difference between 1.75 and.  Use a complete sentence.

6.	Explain why 0.is not an irrational number.

7.	List all the number from the given set that are

a.	natural numbers
b.	whole numbers	c.	integers
d.	rational numbers	e.	irrational numbers
f.	real numbers.	

{-9, }

8.      Place  or  to make each sentence true.
a.	-3 _____ {x | x is an integer}			c.	7 _____ {0, 2, 4, 6, . . . }
b.	 _____ { x | x is an irrational number}	d.	0.7373. . . _____ { x | x is a               	rational number}