This volume explores the consequences of the paradox for measure theory and its connections with group theory, geometry, and logic. It unifies the results of contemporary research on the paradox and presents several new results including some unusual paradoxes in hyperbolic space. It also provides up to date proofs and discusses many unsolved problems.
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"...a readable and stimulating book." Ward Henson, American Scientist
"...packed with fascinating and beautiful results." R.J. Gardner, Bulletin of the London Mathematical Society
"...this beautiful book is written with care and is certainly worth reading." Wlodzimierz Bzyl, Mathematical Reviews
"...packed with fascinating and beautiful results." R.J. Gardner, Bulletin of the London Mathematical Society
"...this beautiful book is written with care and is certainly worth reading." Wlodzimierz Bzyl, Mathematical Reviews
Book Description
Asserting that a solid ball may be taken apart into many pieces that can be rearranged to form a ball twice as large as the original, the Banach-Tarski paradox is examined in relationship to measure and group theory, geometry and logic.
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The Banach-Tarski Paradox,
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This review is from: The Banach-Tarski Paradox (Encyclopedia of Mathematics and its Applications) (Paperback)
If you're really interested in the Banach-Tarski Paradox this book is what you have to read. The straightness of thoughts of Stan Wagon and his beautiful ideas not only about the paradox but also set theorie in general were so impressing, that thi s book became one of my favourites.
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Inside This Book
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First Sentence:
It has been known since antiquity that the notion of infinity leads very quickly to seemingly paradoxical constructions, many of which seem to change the size of objects by operations that appear to preserve size. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
countable equidecomposability, having total measure one, large free groups, asymptotically invariant sequence, commutative free subgroup, topological amenability, independent isometries, free subsemigroup, paradoxical decomposition, commutative free groups, exotic measure, commutative action, finitely additive extension, nontrivial fixed points, nonatomic measure space, paradoxical groups, countable dense subgroup, local commutativity, measurable pieces, type semigroup, nontrivial word, meager sets, using isometries, amenable group, nonmeasurable set Key Phrases - Capitalized Phrases (CAPs): (learn more)
Axiom of Choice, Banach-Tarski Paradox, Property of Baire, Folner's Condition, Invariant Extension Theorem, Hausdorff Paradox, Marczewski's Problem, Measure Extension Theorem, Bolyai-Gerwien Theorem, Hahn-Banach Theorem, Tits's Theorem, Hahn-Banach Extension Property, Milnor-Wolf Conjecture, Ruziewicz's Problem, Ruziewicz Problem, Continuum Hypothesis, Sierpinski-Mazurkiewicz Paradox, Markov-Kakutani Fixed Point Theorem, Sierpifiski-Mazurkiewicz Paradox, Hilbert's Third Problem, Tarski's Circle-Squaring Problem, The Magic Snake, The Scottish Book, Tychonoff Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
It has been known since antiquity that the notion of infinity leads very quickly to seemingly paradoxical constructions, many of which seem to change the size of objects by operations that appear to preserve size. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
countable equidecomposability, having total measure one, large free groups, asymptotically invariant sequence, commutative free subgroup, topological amenability, independent isometries, free subsemigroup, paradoxical decomposition, commutative free groups, exotic measure, commutative action, finitely additive extension, nontrivial fixed points, nonatomic measure space, paradoxical groups, countable dense subgroup, local commutativity, measurable pieces, type semigroup, nontrivial word, meager sets, using isometries, amenable group, nonmeasurable set Key Phrases - Capitalized Phrases (CAPs): (learn more)
Axiom of Choice, Banach-Tarski Paradox, Property of Baire, Folner's Condition, Invariant Extension Theorem, Hausdorff Paradox, Marczewski's Problem, Measure Extension Theorem, Bolyai-Gerwien Theorem, Hahn-Banach Theorem, Tits's Theorem, Hahn-Banach Extension Property, Milnor-Wolf Conjecture, Ruziewicz's Problem, Ruziewicz Problem, Continuum Hypothesis, Sierpinski-Mazurkiewicz Paradox, Markov-Kakutani Fixed Point Theorem, Sierpifiski-Mazurkiewicz Paradox, Hilbert's Third Problem, Tarski's Circle-Squaring Problem, The Magic Snake, The Scottish Book, Tychonoff Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 3
books:
64
books
cite this book:
See all 64 books citing this book
- Provability, Computability and Reflection, Volume 75 (Studies in Logic and the Foundations of Mathematics) by Lev D. Beklemishev on page 114, and Index
- Introduction to Axiomatic Set Theory (Synthese Library) by J.L. Krivine in Index
- The Burnside problem and identities in groups (Ergebnisse der Mathematik und ihrer Grenzgebiete) by S. I Adian in Index
- The Pea and the Sun: A Mathematical Paradox by Leonard M. Wapner on 4 pages
- Math Hysteria: Fun and Games with Mathematics by Ian Stewart on page 77, and Back Matter
- Alfred Tarski: Life and Logic by Anita Burdman Feferman in Back Matter (1), and Back Matter (2)
- Sets, Logic and Categories (Springer Undergraduate Mathematics Series) by Peter J. Cameron on page 122, and Back Matter
- A Primer of Infinitesimal Analysis by John L. Bell on page 105, and Back Matter
See all 64 books citing this book
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