The Banach Tarski Paradox
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The Banach Tarski Paradox
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Author : Stan Wagon
language : en
Publisher:
Release Date : 1985
The Banach Tarski Paradox written by Stan Wagon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Banach-Tarski paradox categories.
The Banach-Tarski paradox is a most striking mathematical construction: it asserts that a solid ball may be taken apart into finitely many pieces that can be rearranged using rigid motions to form a ball twice as large as the original. This volume explore.
The Banach Tarski Paradox
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Author : Stan Wagon
language : en
Publisher: Cambridge University Press
Release Date : 1993-09-24
The Banach Tarski Paradox written by Stan Wagon and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-09-24 with Mathematics categories.
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.
The Banach Tarski Paradox
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Author : Grzegorz Tomkowicz
language : en
Publisher: Cambridge University Press
Release Date : 2016-06-14
The Banach Tarski Paradox written by Grzegorz Tomkowicz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-14 with Mathematics categories.
The Banach-Tarski Paradox seems patently false. The authors explain it and its implications in terms appropriate for an undergraduate.
Banach Tarski Paradox
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Author : Stan Wagon
language : en
Publisher:
Release Date : 1999
Banach Tarski Paradox written by Stan Wagon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
The Banach Tarski Paradox
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Author : Grzegorz Tomkowicz
language : en
Publisher: Cambridge University Press
Release Date : 2016-06-14
The Banach Tarski Paradox written by Grzegorz Tomkowicz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-14 with Mathematics categories.
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 contemporary research on the paradox. It has been updated with many new proofs and results, and discussions of the many problems that remain unsolved. Among the new results presented are several unusual paradoxes in the hyperbolic plane, one of which involves the shapes of Escher's famous 'Angel and Devils' woodcut. A new chapter is devoted to a complete proof of the remarkable result that the circle can be squared using set theory, a problem that had been open for over sixty years.
The Pea And The Sun
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Author : Leonard M. Wapner
language : en
Publisher: CRC Press
Release Date : 2005-04-29
The Pea And The Sun written by Leonard M. Wapner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-29 with Mathematics categories.
Take an apple and cut it into five pieces. Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.
Conjecture And Proof
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Author : Miklós Laczkovich
language : en
Publisher: American Mathematical Society
Release Date : 2022-08-11
Conjecture And Proof written by Miklós Laczkovich and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-11 with Mathematics categories.
The Budapest semesters in mathematics were initiated with the aim of offering undergraduate courses that convey the tradition of Hungarian mathematics to English-speaking students. This book is an elaborate version of the course on Conjecture and Proof. It gives miniature introductions to various areas of mathematics by presenting some interesting and important, but easily accessible results and methods. The text contains complete proofs of deep results such as the transcendence of $e$, the Banach-Tarski paradox and the existence of Borel sets of arbitrary (finite) class. One of the purposes is to demonstrate how far one can get from the first principles in just a couple of steps. Prerequisites are kept to a minimum, and any introductory calculus course provides the necessary background for understanding the book. Exercises are included for the benefit of students. However, this book should prove fascinating for any mathematically literate reader.
On The Brink Of Paradox
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Author : Agustin Rayo
language : en
Publisher: MIT Press
Release Date : 2019-04-02
On The Brink Of Paradox written by Agustin Rayo and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-02 with Mathematics categories.
An introduction to awe-inspiring ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, and computability theory. This book introduces the reader to awe-inspiring issues at the intersection of philosophy and mathematics. It explores ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, computability theory, the Grandfather Paradox, Newcomb's Problem, the Principle of Countable Additivity. The goal is to present some exceptionally beautiful ideas in enough detail to enable readers to understand the ideas themselves (rather than watered-down approximations), but without supplying so much detail that they abandon the effort. The philosophical content requires a mind attuned to subtlety; the most demanding of the mathematical ideas require familiarity with college-level mathematics or mathematical proof. The book covers Cantor's revolutionary thinking about infinity, which leads to the result that some infinities are bigger than others; time travel and free will, decision theory, probability, and the Banach-Tarski Theorem, which states that it is possible to decompose a ball into a finite number of pieces and reassemble the pieces so as to get two balls that are each the same size as the original. Its investigation of computability theory leads to a proof of Gödel's Incompleteness Theorem, which yields the amazing result that arithmetic is so complex that no computer could be programmed to output every arithmetical truth and no falsehood. Each chapter is followed by an appendix with answers to exercises. A list of recommended reading points readers to more advanced discussions. The book is based on a popular course (and MOOC) taught by the author at MIT.
Mathematica In Action
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Author : Stan Wagon
language : en
Publisher: Springer Science & Business Media
Release Date : 1999
Mathematica In Action written by Stan Wagon and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Computers categories.
"Mathematica in Action, 2nd Edition," is designed both as a guide to the extraordinary capabilities of Mathematica as well as a detailed tour of modern mathematics by one of its leading expositors, Stan Wagon. Ideal for teachers, researchers, mathematica enthusiasts. This second edition of the highly sucessful W.H. Freeman version includes an 8 page full color insert and 50% new material all organized around Elementary Topics, Intermediate Applications, and Advanced Projects. In addition, the book uses Mathematica 3.0 throughtout. Mathematica 3.0 notebooks with all the programs and examples discussed in the book are available on the TELOS web site (www.telospub.com). These notebooks contain materials suitable for DOS, Windows, Macintosh and Unix computers. Stan Wagon is well-known in the mathematics (and Mathematica) community as Associate Editor of the "American Mathematical Monthly," a columnist for the "Mathematical Intelligencer" and "Mathematica in Education and Research," author of "The Banach-Tarski Paradox" and "Unsolved Problems in Elementary Geometry and Number Theory (with Victor Klee), as well as winner of the 1987 Lester R. Ford Award for Expository Writing.
Diagonalization In Formal Mathematics
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Author : Paulo Guilherme Santos
language : en
Publisher: Springer Nature
Release Date : 2020-01-04
Diagonalization In Formal Mathematics written by Paulo Guilherme Santos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-04 with Mathematics categories.
In this book, Paulo Guilherme Santos studies diagonalization in formal mathematics from logical aspects to everyday mathematics. He starts with a study of the diagonalization lemma and its relation to the strong diagonalization lemma. After that, Yablo’s paradox is examined, and a self-referential interpretation is given. From that, a general structure of diagonalization with paradoxes is presented. Finally, the author studies a general theory of diagonalization with the help of examples from mathematics.
