Introduction to the Theory of Sets

by Breuer, Joseph; Fehr, Howard F.

• ISBN13: 9780486453101
• ISBN10: 0486453103
• Format: Paperback
• Copyright: 2006-07-28
• Publisher: Dover Publications

Summary

Set theory permeates much of contemporary mathematical thought. This text for undergraduates offers a natural introduction, developing the subject through observations of the physical world. Its progressive development leads from finite sets to cardinal numbers, infinite cardinals, and ordinals. Exercises appear throughout the text, with answers at the end.

Table of Contents

Introduction	1	(3)
Finite Sets	4	(13)
Set, element, equality of sets	4	(3)
Subset, complementary set, union, intersection	7	(5)
Equivalent set, cardinal numbers	12	(5)
Infinite Sets	17	(38)
Equivalence and transfinite cardinal numbers	17	(3)
Denumerable sets	20	(6)
Non-denumerable sets	26	(8)
Further non-denumerable sets	34	(5)
The equivalence theorem	39	(5)
Sums and products of cardinal numbers	44	(5)
Powers of cardinal numbers	49	(6)
Ordered Sets	55	(14)
Ordered sets and order-types	55	(8)
Well-ordered sets and ordinal numbers	63	(6)
Points Sets	69	(14)
Accumulation and condensation points	69	(3)
Closed, dense, and perfect sets	72	(3)
Continuous sets	75	(3)
Range and continuity of functions	78	(5)
Conclusion	83	(10)
The paradoxes of set theory	83	(3)
Formalism and intuitionalism	86	(7)
Appendix	93	(6)
Glossary of definitions and theorems	93	(1)
Brief historical outline	94	(2)
Bibliography	96	(1)
Glossary of symbols	97	(2)
Answers to exercises	99	(6)
Index	105