Proofs of the Cantor-Bernstein Theorem: A Mathematical by Arie Hinkis

March 19, 2017 admin

By Arie Hinkis

This ebook bargains an expedition during the developmental zone of analysis arithmetic. It offers a few forty papers, released among the 1870s and the Nineteen Seventies, on proofs of the Cantor-Bernstein theorem and the similar Bernstein department theorem. whereas the emphasis is put on supplying exact proofs, just like the originals, the dialogue is broadened to incorporate points that pertain to the method of the improvement of arithmetic and to the philosophy of arithmetic. Works of popular mathematicians and logicians are reviewed, together with Cantor, Dedekind, Schröder, Bernstein, Borel, Zermelo, Poincaré, Russell, Peano, the Königs, Hausdorff, Sierpinski, Tarski, Banach, Brouwer and a number of other others often of the Polish and the Dutch faculties. In its try and current a diachronic narrative of 1 mathematical subject, the publication resembles Lakatos’ celebrated publication Proofs and Refutations. certainly, many of the observations made via Lakatos are corroborated herein. The analogy among the 2 books is obviously something yet superficial, because the current e-book additionally bargains new theoretical insights into the method of the advance of arithmetic (proof-processing), with implications for the historiography of mathematics.

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