Proofs of the Cantor-Bernstein Theorem: A Mathematical Excursion: 45 (Science Networks. Historical Studies) - Tapa dura

Hinkis, Arie

 
9783034802239: Proofs of the Cantor-Bernstein Theorem: A Mathematical Excursion: 45 (Science Networks. Historical Studies)
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ISBN 10: 3034802234 ISBN 13: 9783034802239
Editorial: Birkhäuser, 2013

Sinopsis

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.

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De la contraportada

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.

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Editorial
Birkhäuser
Año de publicación
2013
Idioma
Inglés
ISBN 10 
3034802234
ISBN 13 
9783034802239
Encuadernación
Tapa dura
Número de páginas
456
Contacto del fabricante
no disponible
Persona responsable
no disponible

Otras ediciones populares con el mismo título

9783034807883: Proofs of the Cantor-Bernstein Theorem: A Mathematical Excursion: 45 (Science Networks. Historical Studies)

Edición Destacada

ISBN 10:  3034807880 ISBN 13:  9783034807883
Editorial: Birkhäuser, 2015
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