Elementary Set Theory

Kam-Tim Leung, Doris Lai-Chue Chen9622090265, 9789622090262

Table of contents :
Title Page……Page 3
versor……Page 4
Forewordr……Page 5
Prefacer……Page 7
Table of Contentsr……Page 9
PART Ir……Page 11
A. Statements.r……Page 12
B. Conjunctions.r……Page 13
C. Disjunctions.r……Page 14
D. Negations.r……Page 15
E. Conditionals.r……Page 16
G. Iterated compositions.r……Page 17
H. Equivalent formulae.r……Page 19
I. Valid formulae.r……Page 21
K. Implications.r……Page 23
L. The symbols [universal quantifier] and [existential quantifier]. ……Page 26
M. Exercises.r……Page 29
A. Sets.r……Page 31
B. The axiom of extension.r……Page 33
C. Subsets and the empty set.r……Page 34
D. Venn diagrams.r……Page 37
E. Unordered pairs and singletons.r……Page 38
F. Intersections.r……Page 39
G. Unions.r……Page 40
H. Complements.r……Page 42
I. Power sets.r……Page 45
J. Unions and intersections of subsets.r……Page 46
K. Exercises.r……Page 48
A. Ordered pairs.r……Page 52
B. Cartesian products of sets.r……Page 53
C. Relations.r……Page 54
D. Inverses and compositions.r……Page 55
E. Equivalence relations.r……Page 57
F. Exercises.r……Page 60
A. Mappings.r……Page 62
B. Compositions.r……Page 64
C. Direct images and inverse images.r……Page 65
D. Injective, surjective and bijective mappings.r……Page 67
E. Factorizations.r……Page 69
F. Exercises.r……Page 72
PART IIr……Page 74
A. Families.r……Page 75
B. Intersections and unions.r……Page 76
C. Cartesian products.r……Page 78
D. The axiom of choice.r……Page 80
E. Projections.r……Page 82
F. Exercises.r……Page 83
A. Definition.r……Page 85
B. Peano’s axioms.r……Page 86
C. The usual order relation of natural numbers.r……Page 88
D. Recursion theorems.r……Page 90
E. The arithmetic of natural numbers.r……Page 92
F. Integers and Rational numbers.r……Page 95
G. Exercises.r……Page 98
A. Equipotent sets.r……Page 99
B. Finite sets.r……Page 101
C. Countable sets.r……Page 103
D. Infinite sets.r……Page 106
E. Exercises.r……Page 108
A. Order relations.r……Page 110
B. Mappings of ordered sets.r……Page 112
C. Well-ordered sets.r……Page 114
D. The well-ordering principle and its equivalences.r……Page 119
E. Exercises.r……Page 123
A. Ordinal numbers.r……Page 125
B. General properties of ordinal numbers…….Page 126
C. The arithmetic of ordinal numbers.r……Page 129
D. Cardinal numbers.r……Page 131
E. Cantor’s continuum hypothesis.r……Page 133
F. Exercises.r……Page 134
Special Symbols and Abbreviationsr……Page 136
List of Axiomsr……Page 138
Indexr……Page 139