# Proofs of the Cantor-Bernstein Theorem

## A Mathematical Excursion

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

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

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.

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

- DOI https://doi.org/10.1007/978-3-0348-0224-6
- Copyright Information Springer Basel 2013
- Publisher Name Birkhäuser, Basel
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-0348-0223-9
- Online ISBN 978-3-0348-0224-6
- About this book