The Pea and the Sun

A Mathematical Paradox

Author: Leonard M. Wapner

Publisher: A K Peters/CRC Press

ISBN: 9781568813271

Category: Mathematics

Page: 232

View: 2107

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.
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Infinity, Causation, and Paradox

Author: Alexander R. Pruss

Publisher: Oxford University Press

ISBN: 0192538284

Category: Philosophy

Page: 248

View: 9737

Infinity is paradoxical in many ways. Some paradoxes involve deterministic supertasks, such as Thomson's Lamp, where a switch is toggled an infinite number of times over a finite period of time, or the Grim Reaper, where it seems that infinitely many reapers can produce a result without doing anything. Others involve infinite lotteries. If you get two tickets from an infinite fair lottery where tickets are numbered from 1, no matter what number you saw on the first ticket, it is almost certain that the other ticket has a bigger number on it. And others center on paradoxical results in decision theory, such as the surprising observation that if you perform a sequence of fair coin flips that goes infinitely far back into the past but only finitely into the future, you can leverage information about past coin flips to predict future ones with only finitely many mistakes. Alexander R. Pruss examines this seemingly large family of paradoxes in Infinity, Causation and Paradox. He establishes that these paradoxes and numerous others all have a common structure: their most natural embodiment involves an infinite number of items causally impinging on a single output. These paradoxes, he argues, can all be resolved by embracing 'causal finitism', the view that it is impossible for a single output to have an infinite causal history. Throughout the book, Pruss exposits such paradoxes, defends causal finitism at length, and considers connections with the philosophy of physics (where causal finitism favors but does not require discretist theories of space and time) and the philosophy of religion (with a cosmological argument for a first cause).
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A Bridge to Advanced Mathematics

Author: Dennis Sentilles

Publisher: Courier Corporation

ISBN: 0486277585

Category: Mathematics

Page: 416

View: 8611

This helpful "bridge" book offers students the foundations they need to understand advanced mathematics. The two-part treatment provides basic tools and covers sets, relations, functions, mathematical proofs and reasoning, more. 1975 edition.
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Excursions in the History of Mathematics

Author: Israel Kleiner

Publisher: Springer Science & Business Media

ISBN: 0817682686

Category: Mathematics

Page: 347

View: 581

This book comprises five parts. The first three contain ten historical essays on important topics: number theory, calculus/analysis, and proof, respectively. Part four deals with several historically oriented courses, and Part five provides biographies of five mathematicians who played major roles in the historical events described in the first four parts of the work. Excursions in the History of Mathematics was written with several goals in mind: to arouse mathematics teachers’ interest in the history of their subject; to encourage mathematics teachers with at least some knowledge of the history of mathematics to offer courses with a strong historical component; and to provide an historical perspective on a number of basic topics taught in mathematics courses.
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The World of Mathematics

Author: James Roy Newman

Publisher: Courier Corporation

ISBN: 0486411516

Category: Mathematics

Page: 624

View: 1651

Presents 33 essays on such topics as statistics and the design of experiments, group theory, the mathematics of infinity, the mathematical way of thinking, the unreasonableness of mathematics, and mathematics as an art. A reprint of volume 3 of the four-volume edition originally published by Simon and Schuster in 1956. Annotation c. Book News, Inc., Portland, OR (booknews.com).
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The World of Mathematics

Author: James R. Newman

Publisher: Рипол Классик

ISBN: 5881361539

Category: History

Page: 2535

View: 3771

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Mathematics and the Imagination

Author: Edward Kasner,James Roy Newman

Publisher: Courier Corporation

ISBN: 0486417034

Category: Mathematics

Page: 380

View: 6235

Introduces simple arithmetic, calculus, and non-Euclidean geometry through games and puzzles.
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The New Criterion

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Arts

Page: N.A

View: 9916

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