Mathematical Fallacies and Paradoxes

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.

Author: Bryan Bunch

Publisher: Courier Corporation

ISBN: 9780486137933

Category: Mathematics

Page: 240

View: 759


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.

Mathematical Fallacies Flaws and Flimflam

162 Mathematical Fallacies. Flaws, and Flimflam Glenn W. Erickson & John A.
Fossa, Dictionary of paradox. University Press of ... Patrick Hughes & George
Brecht, Vicious circles and infinity: a panoply of paradoxes. Doubleday, New York

Author: Edward Barbeau

Publisher: MAA

ISBN: 0883855291

Category: Mathematics

Page: 167

View: 618


Through hard experience mathematicians have learned to subject even the most 'evident' assertions to rigorous scrutiny, as intuition and facile reasoning can often be misleading. However, errors can slip past the most watchful eye, they are often subtle and difficult to detect; but when found they can teach us a lot and can present a real challenge to straighten out. This book collects together a mass of such errors, drawn from the work of students, textbooks, and the media, as well as from professional mathematicians themselves. Each of these items is carefully analysed and the source of the error is exposed. All serious students of mathematics will find this book both enlightening and entertaining.

Guide to Discrete Mathematics

14.3 Paradoxes and Fallacies A paradox is a statement that apparently
contradicts itself, and it presents a situation that appears to defy logic. Some
logical paradoxes have a solution, whereas others are contradictions or invalid

Author: Gerard O'Regan

Publisher: Springer

ISBN: 9783319445618

Category: Computers

Page: 368

View: 356


This stimulating textbook presents a broad and accessible guide to the fundamentals of discrete mathematics, highlighting how the techniques may be applied to various exciting areas in computing. The text is designed to motivate and inspire the reader, encouraging further study in this important skill. Features: provides an introduction to the building blocks of discrete mathematics, including sets, relations and functions; describes the basics of number theory, the techniques of induction and recursion, and the applications of mathematical sequences, series, permutations, and combinations; presents the essentials of algebra; explains the fundamentals of automata theory, matrices, graph theory, cryptography, coding theory, language theory, and the concepts of computability and decidability; reviews the history of logic, discussing propositional and predicate logic, as well as advanced topics; examines the field of software engineering, describing formal methods; investigates probability and statistics.

Chance Encounters Probability in Education

Paradoxes. and. Fallacies. Though mathematics aims to deal with universal
truths, its progress has not always been smooth. The history of mathematics has
revealed many interesting paradoxes some of which have served as triggers for
great ...

Author: R. Kapadia

Publisher: Springer Science & Business Media

ISBN: 9789401135320

Category: Education

Page: 267

View: 706


This book has been written to fIll a substantial gap in the current literature in mathemat ical education. Throughout the world, school mathematical curricula have incorporated probability and statistics as new topics. There have been many research papers written on specifIc aspects of teaching, presenting novel and unusual approaches to introducing ideas in the classroom; however, there has been no book giving an overview. Here we have decided to focus on probability, making reference to inferential statistics where appropriate; we have deliberately avoided descriptive statistics as it is a separate area and would have made ideas less coherent and the book excessively long. A general lead has been taken from the fIrst book in this series written by the man who, probably more than everyone else, has established mathematical education as an aca demic discipline. However, in his exposition of didactical phenomenology, Freudenthal does not analyze probability. Thus, in this book, we show how probability is able to organize the world of chance and idealized chance phenomena based on its development and applications. In preparing these chapters we and our co-authors have reflected on our own acquisition of probabilistic ideas, analyzed textbooks, and observed and reflect ed upon the learning processes involved when children and adults struggle to acquire the relevant concepts.

Mathematical Spectrum

Gotcha : Paradoxes to Puzzle and Delight . By Martin GARDNER . W . H .
Freeman and Company , San Francisco , 1982 . Pp . vii + 164 . Hardback £11 .
20 . Paperback £5 . 60 . Mathematical Fallacies and Paradoxes . By BRYAN H .



ISBN: UCSD:31822020383477

Category: Mathematics


View: 265


Pragmatics of Human Communication A Study of Interactional Patterns Pathologies and Paradoxes

or fallacies. For instance, Zeno's paradox of Achilles and the turtle he could not
overtake was undoubtedly a “true” paradox ... but most authors prefer to limit its
use to paradoxes arising in formalized systems such as logic and mathematics.

Author: Paul Watzlawick

Publisher: W. W. Norton & Company

ISBN: 9780393707229

Category: Psychology

Page: 304

View: 567


The properties and function of human communication. Called “one of the best books ever about human communication,” and a perennial bestseller, Pragmatics of Human Communication has formed the foundation of much contemporary research into interpersonal communication, in addition to laying the groundwork for context-based approaches to psychotherapy. The authors present the simple but radical idea that problems in life often arise from issues of communication, rather than from deep psychological disorders, reinforcing their conceptual explorations with case studies and well-known literary examples. Written with humor and for a variety of readers, this book identifies simple properties and axioms of human communication and demonstrates how all communications are actually a function of their contexts. Topics covered in this wide-ranging book include: the origins of communication; the idea that all behavior is communication; meta-communication; the properties of an open system; the family as a system of communication; the nature of paradox in psychotherapy; existentialism and human communication.

Supplementary Geometry

Paradoxes. and. Mathematical. Fallacies. A paradox is an assertion which is ( 1 )
self - contradictory , ( 2 ) contradictory to the postulates from which it is deduced
or to other postulates or theorems of the system , or ( 3 ) a true assertion ...

Author: Karl H. West


ISBN: CHI:13092503

Category: Geometry

Page: 134

View: 705


Order and Organism

Steps Toward a Whiteheadian Philosophy of Mathematics and the Natural
Sciences Murray Code. of becoming ... Thus he unnecessarily , and erroneously ,
dismisses the second form of the paradox as based upon a mathematical fallacy .

Author: Murray Code

Publisher: SUNY Press

ISBN: 0873959515

Category: Mathematics

Page: 265

View: 516


What is now needed is a way of thinking about the physical that is realistic in outlook but which departs radically from the mechanistic post-Galilean tradition. Since it seems clear that we can no longer take for granted the certainty and absolute objectivity of scientific knowledge, any alternative view must be able to do full justice to subjective modes of knowing. Order and Organism shows how Alfred North Whitehead's thought can reconcile some of the most insistent demands of common sense with the esoteric results of modern physics and mathematics. Whitehead shows a way to resolve the perennial puzzle of why mathematics works. Under his view, it is possible to account for the necessity and uniqueness of mathematical theories without denying the fact that such theories often arise from the mathematician's essentially aesthetic interest in various kinds of pattern.

The World of Mathematics

-W . S. GILBERT PERHAPS the greatest paradox of all is that there are
paradoxes in mathematics . We are not surprised to ... do arise in mathematics .
There are contradictory and absurd propositions , which arise from fallacious
reasoning .

Author: James Roy Newman

Publisher: Courier Corporation

ISBN: 0486411516

Category: Mathematics

Page: 624

View: 162


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 (


the. fallacy. Amos Tversky and Daniel Kahneman proposed that the gambler's
fallacy is a cognitive bias produced by a ... Thetheorems,
provenbyKurtGödelin1931, areimportantboth in mathematical logic and in the
philosophy of mathematics.


Publisher: PediaPress




View: 802


The High School Mathematics Library

Linn , Charles F . Puzzles , Patterns and Pastimes , from the World of
Mathematics . Doubleday , 1969 ... Emphasis on mathematical paradoxes and
fallacies , including paradoxes of logic , of probability , and of the infinite . ☆ O '
Beirne , T . H ...

Author: William Leonard Schaaf


ISBN: UOM:39015036794736

Category: Mathematics

Page: 74

View: 478


The American Mathematical Monthly

Books submitted for review should be sent to Book Review Editor , American
Mathematical Monthly , St. Olaf College , Northfield , Minnesota 55057 . ... LAS
Mathematics Appreciation , S * ( 13-15 ) , L. Mathematical Fallacies and
Paradoxes .



ISBN: UCSD:31822005895461

Category: Mathematicians


View: 180


The New Encyclopaedia Britannica

see conjugate harmonic function logarithmic spiral , or equiangular spiral , or
logistic spiral ( math . ) ... Carnap 2 : 877 : 3a by Bridgman ) LPC quantifiers 23 :
237 : 16 Chrysippus 25 : 741 : 1a | logical fallacy , or fallacy in discourse
discussed in biography 2 ... Cantor ' s paradox ; mathematical aspects Logical
Positivist philosophy of Russell ' s paradox automata theory 14 : 539 : 16 passim
science 25 : 633 ...

Author: Encyclopaedia Britannica, inc

Publisher: Encyclopedia Britannica Incorporated

ISBN: UOM:39015052983353

Category: Reference

Page: 952

View: 912


Journal of Economic Issues

Mathematical Fallacies and Paradoxes . New York : Van Nostrand Reinhold .
Crouch , Robert L . 1979 . Human Behavior : An Economic ... The Mathematical
Experience . Boston : Houghton Miffin . Dewey , John . 1966 . “ Theory of
Valuation .



ISBN: STANFORD:36105007761740

Category: Economics


View: 995


Mathematics in Secondary Schools Today

KASNER , E. , and NEWMAN , J. Mathematics and the Imagination , Simon and
Schuster , 1940. A treatment of arithmetical and geometrical fallacies and
paradoxes , the underlying idea of calculus and its applications , squaring the
circle , pi ...

Author: National Council of Teachers of Mathematics


ISBN: UOM:39015077959560

Category: Mathematics

Page: 196

View: 982