Contents
BOOK ONE The Foundation: Sets, Logic,
- SETS and Mathematical Argument
- Basic Definitions and Notation
- Operations on Sets
- Algebraic Properties of Sets
- Theorems of Set Theory
- Counting Properties of Finite Sets (Optional)
- LOGIC, PART I: THE PROPOSITIONAL CALCULUS
- Basic Concepts of the Propositional Calculus
- Tautology, Equivalence, the Conditional, and Biconditional
- Theorems of the Propositional Calculus
- Analysis of Arguments for Logical Validity, Part I (Optional)
- LOGIC, PART 11: THE PREDICATE CALCULUS
- Basic Concepts of the Predicate Calculus
- Quantification
- Theorems About Predicates in One Variable
- Quantification of Propositional Functions in Several Variables
- Analysis of Arguments for Logical Validity, Part I1 (Optional)
- Applications of Logic to Set Theory-Some Proofs ELEMENTARY 'APPLICATIONS OF LOGIC 11s
- Infinite Unions and Intersections
- The Limit Concept (Optional)
- PART 1: ELEMENTARY METHODS METHODS OF MATHEMATICAL PROOF,
- Conclusions Involving V, but Not 3 or +. Proof by Transitivity
- Conclusions Involving V and +, but Not