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Elements of Set Theory
1st Edition - April 28, 1977
Author: Herbert B. Enderton
Hardback ISBN:9780122384400
9 7 8 - 0 - 1 2 - 2 3 8 4 4 0 - 0
eBook ISBN:9780080570426
9 7 8 - 0 - 0 8 - 0 5 7 0 4 2 - 6
This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the… Read more
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This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.
Undergraduate students interested in set theory.
Contents
Preface
List of Symbols
Chapter 1 Introduction
Baby Set Theory
Sets—An Informal View
Classes
Axiomatic Method
Notation
Historical Notes
Chapter 2 Axioms and Operations
Axioms
Arbitrary Unions and Intersections
Algebra of Sets
Epilogue
Review Exercises
Chapter 3 Relations and Functions
Ordered Pairs
Relations
n-Ary Relations
Functions
Infinite Cartesian Products
Equivalence Relations
Ordering Relations
Review Exercises
Chapter 4 Natural Numbers
Inductive Sets
Peano's Postulates
Recursion on ω
Arithmetic
Ordering on ω
Review Exercises
Chapter 5 Construction of the Real Numbers
Integers
Rational Numbers
Real Numbers
Summaries
Two
Chapter 6 Cardinal Numbers and the Axiom of Choice