MTH 101

1
MTH 101

• PROFESSOR
• David L. Sonnier
• Lyon 208
• 698-4270
• TEXTBOOK
• Marvin L. Bittinger, Judith A. Beecher -
• College Algebra
• (Available at the Lyon Bookstore)
• On the Web
• http//www.lyon.edu/webdata/users/dsonnier/index.h
  tml
• (contains course information and also my slides
  in PPT, updated after each session)

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The Set of Real Numbers
N
Natural Numbers
1
, 2, 3, . . .
Z
Integers
. . . , 2, 1, 0, 1, 2, . . .
__
3
2
Q
Rational Numbers
4
, 0, 8,

,

, 3.14, 5.27
27

5
3
3
I
Irrational Numbers
2

, ?
7
, 1.414213 . . .

3
2

?
R
Real Numbers
7
, 0,
5

,

, 3.14, 0.33
3

,
3
A-1-75
3
Subsets of the Set of Real Numbers
Natural N
Integers Z
Rational Q
Real R
Q
R
Q
Z
N
N ? Z ? Q ? R
A-1-76
4
Subsets of the Set of Real Numbers
Natural
numbers (N)
Integers (Z)
Zero
Rational
numbers (Q)
Negatives
Real
Noninteger
of natural numbers
numbers (R)
ratios
of integers
Irrational
numbers (I)
N ? Z ? Q ? R
A-1-76
5
Sets

• Set Collection of objects (elements)
• a?A a is an element of A
  a is a member of A
• a?A a is not an element of
  A
• A a1, a2, , an A contains
• Order of elements is meaningless
• It does not matter how often the same element is
  listed.

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Sets of Numbers

• Standard Sets
• Natural numbers N 1, 2, 3,
• Whole numbers N 0, 1, 2, 3,
• Integers Z , -2, -1, 0, 1, 2,
• Positive Integers Z 1, 2, 3, 4,
• Real Numbers R 47.3, -12, ?,
• Rational Numbers Q 1.5, 2.6, -3.8, 15,
  (correct definition will follow)

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Set Builder Notation

• Rational Numbers The integers and all quotients
  of integers (excluding division by 0).
• a and b are integers and b ? 0
• In some cases this is easier than the Roster
  Method
• Irrational Number? Any real number that is not
  rational.

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Properties of Real Numbers
Let R be the set of real numbers and let x, y,
and z be arbitrary elements of R.
Equivalent Expressions
4x 7x 11x
Properties of Addition
Commutative Law ab ba Associative
Law a(bc) (ab) c Additive Identity a0
0a a Additive Inverse -a a a (-a) 0
A-1-77(a)
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Properties of Real Numbers
Theorem 1
For any real number a -1 a - a and (-
a) a
Properties of Multiplication
Commutative ab ba Associative a(bc)
(ab)c Multiplicative Identity a1 1 a
a Distributive a(bc) ab
ac Multiplicative Inverse
A-1-77(a)
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Properties of Real Numbers
For any real numbers a, b and c
a b c if and only if b c a a b a
(-b)
Properties of Subtraction
Distributive Law of multiplicaton over
subtraction a(b-c) ab ac
A-1-77(a)
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Properties of Real Numbers
Theorem 4
For any real number a and any nonzero number b
a b a ( )
1 b
A-1-77(a)
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HOMEWORK!!!!!!
Page 9
1-57, EOO (Every Other Odd) problems (1, 5, 9,
13, ) Or, using set-builder notation x x
1 is a multiple of 4 and x lt 58
A-1-77(a)