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Proofs of the Cantor-Bernstein Theorem

A Mathematical Excursion

  • Arie Hinkis

Part of the Science Networks. Historical Studies book series (SNHS, volume 45)

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. Cantor and Dedekind

    1. Front Matter
      Pages 1-1
    2. Arie Hinkis
      Pages 15-25
    3. Arie Hinkis
      Pages 27-38
    4. Arie Hinkis
      Pages 39-47
    5. Arie Hinkis
      Pages 49-55
    6. Arie Hinkis
      Pages 57-66
    7. Arie Hinkis
      Pages 87-101
  3. The Early Proofs

    1. Front Matter
      Pages 103-103
    2. Arie Hinkis
      Pages 105-116
    3. Arie Hinkis
      Pages 117-124
    4. Arie Hinkis
      Pages 125-128
    5. Arie Hinkis
      Pages 129-138
    6. Arie Hinkis
      Pages 139-152
  4. Under the Logicist Sky

    1. Front Matter
      Pages 153-153
    2. Arie Hinkis
      Pages 155-163
    3. Arie Hinkis
      Pages 165-170
    4. Arie Hinkis
      Pages 185-193
    5. Arie Hinkis
      Pages 195-208
    6. Arie Hinkis
      Pages 209-215
    7. Arie Hinkis
      Pages 217-225
    8. Arie Hinkis
      Pages 227-237
    9. Arie Hinkis
      Pages 239-243
    10. Arie Hinkis
      Pages 245-257
    11. Arie Hinkis
      Pages 259-263
    12. Arie Hinkis
      Pages 265-281
    13. Arie Hinkis
      Pages 283-290
  5. At the Polish School

    1. Front Matter
      Pages 291-291
    2. Arie Hinkis
      Pages 293-302
    3. Arie Hinkis
      Pages 303-307
    4. Arie Hinkis
      Pages 309-316
    5. Arie Hinkis
      Pages 323-328
    6. Arie Hinkis
      Pages 343-355
    7. Arie Hinkis
      Pages 357-359
  6. Other Ends and Beginnings

    1. Front Matter
      Pages 361-361
    2. Arie Hinkis
      Pages 363-365
    3. Arie Hinkis
      Pages 367-385
    4. Arie Hinkis
      Pages 387-400
  7. Back Matter
    Pages 401-429

About this book

Introduction

This book offers an excursion through the developmental area of research mathematics. It presents some 40 papers, published between the 1870s and the 1970s, on proofs of the Cantor-Bernstein theorem and the related Bernstein division theorem. While the emphasis is placed on providing accurate proofs, similar to the originals, the discussion is broadened to include aspects that pertain to the methodology of the development of mathematics and to the philosophy of mathematics. Works of prominent mathematicians and logicians are reviewed, including Cantor, Dedekind, Schröder, Bernstein, Borel, Zermelo, Poincaré, Russell, Peano, the Königs, Hausdorff, Sierpinski, Tarski, Banach, Brouwer and several others mainly of the Polish and the Dutch schools. In its attempt to present a diachronic narrative of one mathematical topic, the book resembles Lakatos’ celebrated book Proofs and Refutations. Indeed, some of the observations made by Lakatos are corroborated herein. The analogy between the two books is clearly anything but superficial, as the present book also offers new theoretical insights into the methodology of the development of mathematics (proof-processing), with implications for the historiography of mathematics.

Keywords

Cantor-Bernstein theorem gestalt in mathematics history of science metaphor in mathematics methodology of mathematics philosophy of science proof-processing

Authors and affiliations

  • Arie Hinkis
    • 1
  1. 1.The Cohn Institute for the History, and Philosophy of Science and IdeasTel Aviv UniversityTel AvivIsrael

Bibliographic information