Proofs of the Cantor-Bernstein Theorem

Arie Hinkis

ISBN 10: 3034802234 / ISBN 13: 9783034802239

Editore: Springer Basel, Birkhäuser Basel Mär 2013, 2013

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This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 456 pp. Englisch.

Codice articolo 9783034802239

Dati bibliografici

• Titolo: Proofs of the Cantor-Bernstein Theorem
• Editore: Springer Basel, Birkhäuser Basel Mär 2013
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 3034802234
• ISBN 13: 9783034802239
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 29 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 29 millimetri di profondità
• Peso: 846 grammi

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Riassunto

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.