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section A.1 Real Numbers
Basic number sets and their notations.
(1)  = set of natural numbers = 1, 2, 3, 4, 5, .....
(2) –= set of whole numbers = 0, 1, 2, 3, 4, 5, .....
(3) ™ = set of integers = .....  5,  4,  3,  2,  1, 0, 1, 2, 3, 4, 5, .....
(4)  = set of rational numbers =  n  m, n − ™, n Á 0 = x x is a terminating decimal or repeating deci
(5) (‘  ) = set of irrational numbers = x x is not rational=x x is a non-terminating nonrepeating decim
m
(6) ‘ = set of real numbers
Subset relations:
§–§™§§‘
Ex1,
Is 0.1 a rational number?
Is 0.11 a rational number?
Is 0.111 a rational number?
Ex2,
Is 0.1 a rational number?
Ex3,
Order the following numbers on a number line:
Ex4,
Order the following numbers on a number line:
Ex5,
Show the following numbers on a number line:
Ex6,
Order the following numbers from low to high:
Def
(Absolute value)
Ex7,
Simplify
Ex8,
Simplify
Ex9,
Simplify
Thm
(1) Set of natural numbers is closed under addition and multiplication.
(2) Set of natural numbers is Not closed under subtraction and division.
Thm
(1) Set of integers is closed under addition and subtraction.
(2) Set of integers is Not closed under multiplication and division.
Thm
Set of rational numbers is closed under addition, subtraction, multiplication, and division (except by dividing by
Thm
Set of real numbers is closed under addition, subtraction, multiplication, and division (except by dividing by 0)
x=
x
x
2.7, 7,
4.5, 20,
9
8,
8
3
41
9
3.2 ,  1 16 ,
5
8,
1
9
0.62, 35 , 23 , 0.623
when x 0
when x  0
5
 33  5 
 5  33 
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