Proofs of the Cantor-Bernstein Theorem

A Mathematical Excursion

Nonfiction, Science & Nature, Mathematics, Logic, History
Cover of the book Proofs of the Cantor-Bernstein Theorem by Arie Hinkis, Springer Basel
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Arie Hinkis ISBN: 9783034802246
Publisher: Springer Basel Publication: February 26, 2013
Imprint: Birkhäuser Language: English
Author: Arie Hinkis
ISBN: 9783034802246
Publisher: Springer Basel
Publication: February 26, 2013
Imprint: Birkhäuser
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer Basel

Cover of the book And Yet It Is Heard by Arie Hinkis
Cover of the book Viral Infections of the Human Nervous System by Arie Hinkis
Cover of the book The Scholar and the State: In Search of Van der Waerden by Arie Hinkis
Cover of the book Antimicrobial Peptides and Innate Immunity by Arie Hinkis
Cover of the book Matrix Metalloproteinase Inhibitors by Arie Hinkis
Cover of the book Real Quaternionic Calculus Handbook by Arie Hinkis
Cover of the book Einführung in die angewandte Geometrie by Arie Hinkis
Cover of the book Counting Surfaces by Arie Hinkis
Cover of the book The Inflammasomes by Arie Hinkis
Cover of the book Fractal Symmetry of Protein Exterior by Arie Hinkis
Cover of the book T Lymphocytes as Tools in Diagnostics and Immunotoxicology by Arie Hinkis
Cover of the book Towards a General Theory of Classifications by Arie Hinkis
Cover of the book Bortezomib in the Treatment of Multiple Myeloma by Arie Hinkis
Cover of the book Microlocal Methods in Mathematical Physics and Global Analysis by Arie Hinkis
Cover of the book Kripke’s Worlds by Arie Hinkis
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy