Paradoxes In Mathematics
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Mathematical Fallacies And Paradoxes
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Author : Bryan Bunch
language : en
Publisher: Courier Corporation
Release Date : 1997-07-01
Mathematical Fallacies And Paradoxes written by Bryan Bunch and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-07-01 with Mathematics categories.
Stimulating, thought-provoking analysis of the most interesting intellectual inconsistencies in mathematics, physics, and language, including being led astray by algebra (De Morgan's paradox). 1982 edition.
Paradoxes And Inconsistent Mathematics
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Author : Zach Weber
language : en
Publisher: Cambridge University Press
Release Date : 2021-10-21
Paradoxes And Inconsistent Mathematics written by Zach Weber 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 2021-10-21 with Mathematics categories.
Logical paradoxes – like the Liar, Russell's, and the Sorites – are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses “dialetheic paraconsistency” – a formal framework where some contradictions can be true without absurdity – as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber directly addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary.
Sleight Of Mind
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Author : Matt Cook
language : en
Publisher: MIT Press
Release Date : 2021-08-03
Sleight Of Mind written by Matt Cook and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-03 with Mathematics categories.
This “fun, brain-twisting book . . . will make you think” as it explores more than 75 paradoxes in mathematics, philosophy, physics, and the social sciences (Sean Carroll, New York Times–bestselling author of Something Deeply Hidden). Paradox is a sophisticated kind of magic trick. A magician’s purpose is to create the appearance of impossibility, to pull a rabbit from an empty hat. Yet paradox doesn’t require tangibles, like rabbits or hats. Paradox works in the abstract, with words and concepts and symbols, to create the illusion of contradiction. There are no contradictions in reality, but there can appear to be. In Sleight of Mind, Matt Cook and a few collaborators dive deeply into more than 75 paradoxes in mathematics, physics, philosophy, and the social sciences. As each paradox is discussed and resolved, Cook helps readers discover the meaning of knowledge and the proper formation of concepts—and how reason can dispel the illusion of contradiction. The journey begins with “a most ingenious paradox” from Gilbert and Sullivan’s Pirates of Penzance. Readers will then travel from Ancient Greece to cutting-edge laboratories, encounter infinity and its different sizes, and discover mathematical impossibilities inherent in elections. They will tackle conundrums in probability, induction, geometry, and game theory; perform “supertasks”; build apparent perpetual motion machines; meet twins living in different millennia; explore the strange quantum world—and much more.
Paradoxes
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Author : Hamza E. Alsamraee
language : en
Publisher: Curious Math Publications
Release Date : 2020-09-10
Paradoxes written by Hamza E. Alsamraee and has been published by Curious Math Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-10 with Mathematics categories.
Does .999?=1? Can you cut and reassemble a sphere into two identically sized spheres? Is the consistency of mathematical systems unprovable? Surprisingly, the answer to all of these questions is yes! And at the heart of each question, there lies paradox. For millennia, paradoxes have shaped mathematics and guided mathematical progress forwards. From the ancient paradoxes of Zeno to the modern paradoxes of Russell, paradoxes remind us of the constant need to revamp our mathematical understanding. It is for this reason that paradoxes are so important. Paradoxes: Guiding Forces in Mathematical Exploration provides a survey of mathematical paradoxes spanning a wide variety of topics. It delves into each paradox mathematically, philosophically, and historically, and attempts to provide a full picture of how paradoxes contributed to the progress of mathematics and guided it in many ways. In addition, it discusses how paradoxes can be useful as educational tools. All of that, plus the fact that it is written in a way that is accessible to anyone with a high school background in mathematics! Entertaining and educational, this book will appeal to any reader looking for a mathematical and philosophical challenge.
Riddles In Mathematics
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Author : Eugene P Northrop
language : en
Publisher: Courier Corporation
Release Date : 2014-08-20
Riddles In Mathematics written by Eugene P Northrop and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-20 with Juvenile Nonfiction categories.
"Math enthusiasts of all ages will delight in this collection of more than 200 riddles drawn from every mathematical discipline. Only an elementary background is needed to enjoy and solve the tremendous variety of puzzles, which include riddles based on geometry, trigonometry, algebra, infinity, probability, and logic. Includes complete solutions and 113 illustrations"--
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.
Impossible Folding Puzzles And Other Mathematical Paradoxes
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Author : Gianni A. Sarcone
language : en
Publisher: Courier Corporation
Release Date : 2014-05-25
Impossible Folding Puzzles And Other Mathematical Paradoxes written by Gianni A. Sarcone and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-25 with Games & Activities categories.
Fun-filled, math-based puzzles include Elephants and Castles, Trianglized Kangaroo, Honest Dice and Logic Dice, Mind-reading Powers, and dozens more. Complete solutions explain the mathematical realities behind the fantastic-sounding challenges.
Inconsistent Mathematics
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Author : C.E. Mortensen
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-11-30
Inconsistent Mathematics written by C.E. Mortensen 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 1994-11-30 with Mathematics categories.
without a properly developed inconsistent calculus based on infinitesimals, then in consistent claims from the history of the calculus might well simply be symptoms of confusion. This is addressed in Chapter 5. It is further argued that mathematics has a certain primacy over logic, in that paraconsistent or relevant logics have to be based on inconsistent mathematics. If the latter turns out to be reasonably rich then paraconsistentism is vindicated; while if inconsistent mathematics has seri ous restriytions then the case for being interested in inconsistency-tolerant logics is weakened. (On such restrictions, see this chapter, section 3. ) It must be conceded that fault-tolerant computer programming (e. g. Chapter 8) finds a substantial and important use for paraconsistent logics, albeit with an epistemological motivation (see this chapter, section 3). But even here it should be noted that if inconsistent mathematics turned out to be functionally impoverished then so would inconsistent databases. 2. Summary In Chapter 2, Meyer's results on relevant arithmetic are set out, and his view that they have a bearing on G8del's incompleteness theorems is discussed. Model theory for nonclassical logics is also set out so as to be able to show that the inconsistency of inconsistent theories can be controlled or limited, but in this book model theory is kept in the background as much as possible. This is then used to study the functional properties of various equational number theories.
Puzzles Paradoxes And Problem Solving
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Author : Marilyn A. Reba
language : en
Publisher: CRC Press
Release Date : 2014-12-15
Puzzles Paradoxes And Problem Solving written by Marilyn A. Reba and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-15 with Mathematics categories.
A Classroom-Tested, Alternative Approach to Teaching Math for Liberal Arts Puzzles, Paradoxes, and Problem Solving: An Introduction to Mathematical Thinking uses puzzles and paradoxes to introduce basic principles of mathematical thought. The text is designed for students in liberal arts mathematics courses. Decision-making situations that progress
One Equals Zero And Other Mathematical Surprises
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Author : Nitsa Movshovitz-Hadar
language : en
Publisher: Lawrence Erlbaum Associates
Release Date : 2013
One Equals Zero And Other Mathematical Surprises written by Nitsa Movshovitz-Hadar and has been published by Lawrence Erlbaum Associates this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematical recreations categories.
"Originally published by Key Curriculum Press"--t.p.