The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned course produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so that students studying under the guidance of a tutor may be assessed.
Author(s): Derek C. Goldrei
Series: Chapman & Hall Mathematics
Edition: 1
Publisher: Springer
Year: 1996
Language: English
Pages: 296
Front Matter......Page _002.djvu
Contents......Page _003.djvu
Preface......Page _005.djvu
1.1 Outline of the book......Page 001.djvu
1.2 Assumed knowledge......Page 003.djvu
2.1 Introduction......Page 007.djvu
2.2 Dedekind's construction......Page 008.djvu
2.3 Alternative constructions......Page 017.djvu
2.4 The rational numbers......Page 028.djvu
3.1 Introduction......Page 033.djvu
3.2 The construction of the natural numbers......Page 038.djvu
3.3 Arithmetic......Page 048.djvu
3.4 Finite sets......Page 058.djvu
4.1 Introduction......Page 066.djvu
4.2 A formal language......Page 071.djvu
4.3 Axioms 1 to 3......Page 075.djvu
4.4 Axioms 4 to 6......Page 081.djvu
4.5 Axioms 7 to 9......Page 092.djvu
5.1 Introduction......Page 104.djvu
5.2 The axiom of choice......Page 107.djvu
5.3 The axiom of choice and mathematics......Page 112.djvu
5.4 Zorn's lemma......Page 117.djvu
6.1 Introduction......Page 127.djvu
6.2 Comparing sizes......Page 128.djvu
6.3 Basic properties of ~~ and <=......Page 133.djvu
6.4 Infinite sets without AC - countable sets......Page 140.djvu
6.5 Uncountable sets and cardinal arithmetic without AC......Page 151.djvu
7.1 Introduction......Page 163.djvu
7.2 Linearly ordered sets......Page 164.djvu
7.3 Order arithmetic......Page 177.djvu
7.4 Well-ordered sets......Page 188.djvu
8.1 Introduction......Page 202.djvu
8.2 Ordinal numbers......Page 203.djvu
8.3 Beginning ordinal arithmetic......Page 218.djvu
8.4 Ordinal arithmetic......Page 231.djvu
8.5 The Alephs......Page 254.djvu
9.1 Introduction......Page 263.djvu
9.2 The well-ordering principle......Page 264.djvu
9.3 Cardinal arithmetic and the axiom of choice......Page 267.djvu
9.4 The continuum hypothesis......Page 276.djvu
Bibliography......Page 281.djvu
Index......Page 283.djvu
