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Tables of Contents for Numbers, Sets and Axioms
Chapter/Section Title
Page #
Page Count
Preface
vii

Numbers
1
50
Natural numbers and integers
1
17
Rational numbers
18
8
Real numbers
26
17
Decimal notation
43
8
The size of a set
51
31
Finite and countable sets
51
12
Uncountable sets
63
10
Cardinal numbers
73
9
Ordered sets
82
26
Order relations and ordered sets
82
15
Lattices and Boolean algebras
97
11
Set theory
108
55
What is a set?
108
7
The Zermelo-Fraenkel axioms
115
14
Mathematics in ZF
129
16
Sets and classes
145
11
Models of set theory
156
7
The axiom of choice
163
29
The axiom of choice and direct applications
163
8
Zorn's lemma and the well-ordering theorem
171
13
Other consequences of the axiom of choice
184
8
Ordinal and cardinal numbers
192
45
Well-ordered sets and ordinal numbers
192
13
Transfinite recursion and ordinal arithmetic
205
16
Cardinal numbers
221
16
Hints and solutions to selected exercises
237
10
References
247
2
Index of symbols
249
3
Subject index
252