Proofs of the Cantor-Bernstein Theorem : A Mathematical Excursion

Arie Hinkis

ISBN 10: 3034807880 / ISBN 13: 9783034807883

Edité par Springer Basel, 2015

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - 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.

N° de réf. du vendeur 9783034807883

Détails bibliographiques

• Titre: Proofs of the Cantor-Bernstein Theorem : A Mathematical Excursion
• Éditeur: Springer Basel
• Date de parution: 2015
• Langue: anglais
• ISBN à 10 chiffres: 3034807880
• ISBN à 13 chiffres: 9783034807883
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 235 L x 155 H x 25 P (en millimètres) 235 millimètres de largeur par 155 millimètres de hauteur par 25 millimètres de profondeur
• Poids: 686 grammes

A propos de ce titre

Synopsis

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.

Présentation de l'éditeur

This ‘excursion’ through the evolution of research mathematics takes in some 40 papers, published up to the 1970s, on proofs of the Cantor-Bernstein theorem. It provides a detailed example of proof-processing in the derivation of Bernstein’s division theorem.