Naive Set Theory /
Halmos, P. R.
Naive Set Theory / P. R. Halmos - New York : Springer, 1960. - 104p.: ill.: 9 x 6 x 0.3 in (22.86 x 15.24 x 0.76 cm)
The Axiom of Extension
Paul R. Halmos -Pages 1-3
The Axiom of Specification
Paul R. Halmos
Pages 4-7
Unordered Pairs
Paul R. Halmos
Pages 8-11
Unions and Intersections
Paul R. Halmos
Pages 12-16
Complements and Powers
Paul R. Halmos
Pages 17-21
Ordered Pairs
Paul R. Halmos
Pages 22-25
Relations
Paul R. Halmos
Pages 26-29
Functions
Paul R. Halmos
Pages 30-33
Families
Paul R. Halmos
Pages 34-37
Inverses and Composites
Paul R. Halmos
Pages 38-41
Numbers
Paul R. Halmos
Pages 42-45
The Peano Axioms
Paul R. Halmos
Pages 46-49
Arithmetic
Paul R. Halmos
Pages 50-53
Order
Paul R. Halmos
Pages 54-58
The Axiom of Choice
Paul R. Halmos
Pages 59-61
Zorn’s Lemma
Paul R. Halmos
Pages 62-65
Well Ordering
Paul R. Halmos
Pages 66-69
Transfinite Recursion
Paul R. Halmos
Pages 70-73
Ordinal Numbers
Paul R. Halmos
Pages 74-77
Sets of Ordinal Numbers
Paul R. Halmos
Pages 78-80
Ordinal Arithmetic
Paul R. Halmos
Pages 81-85
The Schröder-Bernstein Theorem
Paul R. Halmos
Pages 86-89
Countable Sets
Paul R. Halmos
Pages 90-93
Cardinal Arithmetic
Paul R. Halmos
Pages 94-98
Cardinal Numbers
Paul R. Halmos -Pages 99-102
Back Matter -Pages 102-104
Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. This book contains my answer to that question. The purpose of the book is to tell the beginning student of advanced mathematics the basic set theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or manifolds. From this point of view the concepts and methods of this book are merely some of the standard mathematical tools; the expert specialist will find nothing new here. Scholarly bibliographical credits and references are out of place in a purely expository book such as this one. The student who gets interested in set theory for its own sake should know, however, that there is much more to the subject than there is in this book. One of the most beautiful sources of set-theoretic wisdom is still Hausdorff's Set theory. A recent and highly readable addition to the literature, with an extensive and up-to-date bibliography, is Axiomatic set theory by Suppes.
9780387900926
Mathematics
511.3 / HAL
Naive Set Theory / P. R. Halmos - New York : Springer, 1960. - 104p.: ill.: 9 x 6 x 0.3 in (22.86 x 15.24 x 0.76 cm)
The Axiom of Extension
Paul R. Halmos -Pages 1-3
The Axiom of Specification
Paul R. Halmos
Pages 4-7
Unordered Pairs
Paul R. Halmos
Pages 8-11
Unions and Intersections
Paul R. Halmos
Pages 12-16
Complements and Powers
Paul R. Halmos
Pages 17-21
Ordered Pairs
Paul R. Halmos
Pages 22-25
Relations
Paul R. Halmos
Pages 26-29
Functions
Paul R. Halmos
Pages 30-33
Families
Paul R. Halmos
Pages 34-37
Inverses and Composites
Paul R. Halmos
Pages 38-41
Numbers
Paul R. Halmos
Pages 42-45
The Peano Axioms
Paul R. Halmos
Pages 46-49
Arithmetic
Paul R. Halmos
Pages 50-53
Order
Paul R. Halmos
Pages 54-58
The Axiom of Choice
Paul R. Halmos
Pages 59-61
Zorn’s Lemma
Paul R. Halmos
Pages 62-65
Well Ordering
Paul R. Halmos
Pages 66-69
Transfinite Recursion
Paul R. Halmos
Pages 70-73
Ordinal Numbers
Paul R. Halmos
Pages 74-77
Sets of Ordinal Numbers
Paul R. Halmos
Pages 78-80
Ordinal Arithmetic
Paul R. Halmos
Pages 81-85
The Schröder-Bernstein Theorem
Paul R. Halmos
Pages 86-89
Countable Sets
Paul R. Halmos
Pages 90-93
Cardinal Arithmetic
Paul R. Halmos
Pages 94-98
Cardinal Numbers
Paul R. Halmos -Pages 99-102
Back Matter -Pages 102-104
Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. This book contains my answer to that question. The purpose of the book is to tell the beginning student of advanced mathematics the basic set theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or manifolds. From this point of view the concepts and methods of this book are merely some of the standard mathematical tools; the expert specialist will find nothing new here. Scholarly bibliographical credits and references are out of place in a purely expository book such as this one. The student who gets interested in set theory for its own sake should know, however, that there is much more to the subject than there is in this book. One of the most beautiful sources of set-theoretic wisdom is still Hausdorff's Set theory. A recent and highly readable addition to the literature, with an extensive and up-to-date bibliography, is Axiomatic set theory by Suppes.
9780387900926
Mathematics
511.3 / HAL