Georg Cantor His Mathematics and Philosophy of the Infinite~tqw~_darksiderg

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INFO

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Title................: Georg Cantor His Mathematics and Philosophy of the

Infinite

Type.................: Ebook

Reader...............: PDF Reader

Size.................: 27 MB

Torrent Hash.........: 35D6B9353E854EAE46833A170A11B9628BD6B343

Posted by............: ~tqw~



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CONTENTS

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Synopsis:

One of the greatest revolutions in mathematics occurred when Georg Cantor

(1845-1918) promulgated his theory of transfinite sets. This revolution is

the subject of Joseph Dauben's important studythe most thorough yet written

of the philosopher and mathematician who was once called a "corrupter of

youth" for an innovation that is now a vital component of elementary school

curricula.Set theory has been widely adopted in mathematics and philosophy,

but the controversy surrounding it at the turn of the century remains of

great interest. Cantor's own faith in his theory was partly theological. His

religious beliefs led him to expect paradoxes in any concept of the

infinite, and he always retained his belief in the utter veracity of

transfinite set theory. Later in his life, he was troubled by recurring

attacks of severe depression. Dauben shows that these played an integral part

in his understanding and defense of set theory.



Table Of Contents:

Introduction 1

1 Preludes in Analysis 6

2 The Origins of Cantorian Set Theory: Trigonometric Series,

Real Numbers, and Derived Sets 30

3 Denumerability and Dimension 47

4 Cantor's Early Theory of Point Sets 77

5 The Mathematics of Cantor's Grundlagen 95

6 Cantor's Philosophy of the Infinite 120

7 From the Grundlagen to the Beitrage, 1883-1895 149

8 The Beitrage, Part I: The Study of Simply-Ordered Sets 169

9 The Beitrage, Part II: The Study of Well-Ordered Sets 194

10 The Foundations and Philosophy of Cantorian Set Theory 219

11 The Paradoxes and Problems of Post-Cantorian Set Theory 240

12 Epilogue: The Significance of Cantor's Personality 271

Appendixes: Previously Unpublished Correspondence 303

Notes 315

Bibliography 361

Index 385



Product Details:

* Pub. Date: September 1990

* Publisher: Princeton University Press

* Format: Paperback, 424pp

* ISBN-13: 9780691024479

* ISBN: 0691024472

* Edition Description: Reprint



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