Introduction to Abstract Mathematics

¿PrefaceAcknowledgmentsI. Logic and Set Theory 1.1 Introduction 1.2 Statements and Open Sentences Exercises 1.2 1.3 Sets Exercises 1.3 1.4 Ordered Pairs and Relations Exercises 1.4 1.5 Functions and Kindred Matters Exercises 1.5 1.6 Axiom Systems and Methods of ProofII. The Natural Numbers 2.1 Introduction 2.2 Arithmetic Exercises 2.2 2.3 Ordering Exercises 2.3III. The Integers and the Rational Numbers 3.1 Introduction 3.2 Preliminaries Exercises 3.2 3.3 Additional Topics Exercises 3.3 3.4 The Rational Numbers and Ordered Fields Exercises 3.4IV. The Real and Complex Numbers 4.1 Introduction 4.2 Construction of R Exercises 4.2V. Metric Spaces 5.1 Introduction 5.2 Definition and Basic Properties Exercises 5.2 5.3 Openness, Closedness, and Neighborhood Systems Exercises 5.3 5.4 Continuous Functions Exercises 5.4VI. Limits 6.1 Introduction Exercise 6.1 6.2 Generalized Limits Exercises 6.2 6.3 Some Examples Exercises 6.3ReferencesAnswers to Selected ExercisesSubject Index