By Arie Hinkis

ISBN-10: 3034802234

ISBN-13: 9783034802239

ISBN-10: 3034807880

ISBN-13: 9783034807883

This booklet bargains an expedition throughout the developmental sector of analysis arithmetic. It provides a few forty papers, released among the 1870s and the Seventies, on proofs of the Cantor-Bernstein theorem and the comparable Bernstein department theorem. whereas the emphasis is put on delivering actual 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 in demand mathematicians and logicians are reviewed, together with Cantor, Dedekind, Schröder, Bernstein, Borel, Zermelo, Poincaré, Russell, Peano, the Königs, Hausdorff, Sierpinski, Tarski, Banach, Brouwer and several other others generally of the Polish and the Dutch colleges. In its try and current a diachronic narrative of 1 mathematical subject, the booklet resembles Lakatos’ celebrated booklet Proofs and Refutations. certainly, a number of the observations made through Lakatos are corroborated herein. The analogy among the 2 books is obviously whatever yet superficial, because the current booklet additionally deals new theoretical insights into the method of the advance of arithmetic (proof-processing), with implications for the historiography of mathematics.