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Proofs of the Cantor-Bernstein Theorem - A Mathematical Excursion (English, Hebrew, Hardcover, 2013 ed.) Loot Price: R4,365
Discovery Miles 43 650
Proofs of the Cantor-Bernstein Theorem - A Mathematical Excursion (English, Hebrew, Hardcover, 2013 ed.): Arie Hinkis

Proofs of the Cantor-Bernstein Theorem - A Mathematical Excursion (English, Hebrew, Hardcover, 2013 ed.)

Arie Hinkis

Series: Science Networks. Historical Studies, 45

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Loot Price R4,365 Discovery Miles 43 650 | Repayment Terms: R409 pm x 12*

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The chief purpose of the book is to present, in detail, a compilation of proofs of the Cantor-Bernstein Theorem (CBT) published through the years since the 1870's. Over thirty such proofs are surveyed.

The book comprises five parts. In the first part the discussion covers the role of CBT and related notions in the writings of Cantor and Dedekind. New views are presented, especially regarding the general proof of CBT obtained by Cantor, his proof of the Comparability Theorem, the ruptures in the Cantor-Dedekind correspondence and the origin of Dedekind's proof of CBT.

The second part covers the first CBT proofs published (1896-1901). The works of the following mathematicians is considered in detail: Schroder, Bernstein, Bore, Schoenflies and Zermelo. Here a subtheme of the book is launched; it concerns the research project following Bernstein's Division Theorem (BDT).

In its third part the book covers proofs that emerged during the period when the logicist movement was developed (1902-1912). It covers the works of Russell and Whitehead, Jourdain, Harward, Poincare, J. Konig, D. Konig (his results in graph theory), Peano, Zermelo, Korselt. Also Hausdorff's paradox is discussed linking it to BDT.

In the fourth part of the book are discussed the developments of CBT and BDT (including the inequality-BDT) in the hands of the mathematicians of the Polish School of Logic, including Sierpi ski, Banach, Tarski, Lindenbaum, Kuratowski, Sikorski, Knaster, the British Whittaker, and Reichbach.

Finally, in the fifth part, the main discussion concentrates on the attempts to port CBT to intuitionist mathematics (with results by Brouwer, Myhill, van Dalen and Troelstra) and to Category Theory (by Trnkova and Koubek).The second purpose of the book is to develop a methodology for the comparison of proofs. The core idea of this methodology is that a proof can be described by two descriptors, called gestalt and metaphor. It is by comparison of their descriptors that the comparison of proofs is obtained. The process by which proof descriptors are extracted from a proof is named 'proof-processing', and it is conjectured that mathematicians perform proof-processing habitually, in the study of proofs.

General

Imprint: Birkhauser Verlag AG
Country of origin: Switzerland
Series: Science Networks. Historical Studies, 45
Release date: March 2013
First published: 2013
Authors: Arie Hinkis
Dimensions: 235 x 155 x 30mm (L x W x T)
Format: Hardcover
Pages: 429
Edition: 2013 ed.
ISBN-13: 978-3-03-480223-9
Languages: English • Hebrew
Categories: Books > Science & Mathematics > Mathematics > History of mathematics
Books > Science & Mathematics > Mathematics > Mathematical foundations > Set theory
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LSN: 3-03-480223-4
Barcode: 9783034802239

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