epdf.pub_the-nuts-and-bolts-of-proofs-third-edition-an-intr

Contents
List of Symbols v
Preface xi
Introduction and Basic Terminology 1
General Suggestions 5
Basic Techniques to Prove If/Then Statements 9
Direct Proof 12
Related Statements 19
Proof by Contrapositive (AKA Proof by Contradiction or
Indirect Proof) 22
How to Construct the Negation of a Statement 25
Special Kinds of Theorems 35
"If and Only If" or "Equivalence Theorems" 35
Use of Counterexamples 45
Mathematical Induction 48
Existence Theorems 58
Uniqueness Theorems 61
Equality of Sets 68
EquaUty of Numbers 78