Addition and Subtraction of Integers

1
Addition and Subtraction of Integers

• Section 5.2

2
Theorems

• Let m and n be positive integers. Then the
  following are true
• (-m)(-n)-(mn)
• If mgtn then m(-n)m-n
• If ngtm then m(-n)-(n-m)
• n(-n)(-n)n0

3
Properties of Integers

• Closure Property
• Commutative Property
• Associative Property
• Additive Identity Property of Zero
• Existence of Negative

4
Definitions

• Let a and b be integers.
• If altb then there exists a c s.t. acb
• b-ac iff acb

5
More Theorems

• The Law of Trichotomy
• One of these must be true
• altb or ab or agtb
• Subtracting by Adding the Negative
• a-ba(-b)

6
Homework

• Pg 311-316
• 1, 2, 3, 4, 6, 9, 11, 13, 35