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The Banach-Tarski paradox

Author: Grzegorz Tomkowicz; S Wagon
Publisher: New York, NY : Cambridge University Press, 2016. ©2016
Series: Encyclopedia of mathematics and its applications, v. 163.
Edition/Format:   eBook : Document : English : Second editionView all editions and formats
Summary:
The Banach--Tarski Paradox is a most striking mathematical construction: it asserts that a solid ball can be taken apart into finitely many pieces that can be rearranged using rigid motions to form a ball twice as large. This volume explores the consequences of the paradox for measure theory and its connections with group theory, geometry, set theory, and logic. This new edition of a classic book unifies  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Tomkowicz, Grzegorz.
Banach-Tarski paradox.
New York, NY : Cambridge University Press, 2016
(DLC) 2015046410
(OCoLC)930786525
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Grzegorz Tomkowicz; S Wagon
ISBN: 9781107337145 1107337143
OCLC Number: 951645109
Notes: Previous edition: The Banach-Tarski paradox / Stan Wagon (Cambridge : Cambridge University Press, 1985).
Description: 1 online resource (xviii, 348 pages) : illustrations (some color).
Contents: Introduction --
The Hausdorff paradox --
The Banach-Tarski paradox: duplicating spheres and balls --
Hyperbolic paradoxes --
Locally commutative actions: Minimizing the number of pieces in a paradoxical decomposition --
Higher dimensions --
Free groups of large rank: Getting a continuum of spheres from one --
Paradoxes in low dimensions --
Squaring the circle --
The semigroup of equidecomposability types --
Transition --
Measures in groups --
Applications of amenability --
Growth conditions in groups and supramenability --
The role of the axiom of choice.
Series Title: Encyclopedia of mathematics and its applications, v. 163.
Responsibility: Grzegorz Tomkowicz, Centrum Edukacji G2, Bytom, Poland, Stan Wagon, Macalester College, St. Paul, Minnesota.

Abstract:

The Banach-Tarski Paradox is the most surprising result in mathematics. This new edition of a classic book offers a comprehensive, accessible presentation, with many related results, especially  Read more...

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'The new edition of The Banach-Tarski Paradox, by Grzegorz Tomkowicz and Stan Wagon, is a welcome revisiting and extensive reworking of the first edition of the book. Whether you are new to the topic Read more...

 
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