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[资源] 【分享】Mathematical Fallacies and Paradoxes.Dover.1982【已搜无重复】

Mathematical Fallacies and Paradoxes
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Authors(Editors):
Bryan Bunch
Publisher: Dover
Pub Date: 1982
Pages: 224
ISBN: 0-486-29664-4
Preface
This book is a collection and analysis of the most interesting paradoxes
and fallacies from mathematics, logic, physics, and language.
It also treats important results in mathematics that are based in paradox,
notably GOdel's theorem of 1931 and decision problems in
general.
The material is arranged so that the rather tenuous relationship
between mathematical reality and physical reality becomes the subject
of the book, while the paradoxes and fallacies are tools for exploring
this relationship. As a result, although the material contains
a number of topics that are often presented in an anthology format,
there is a definite progression from the first chapter to the eighth. It
is possible, however, to read most of the individual paradoxes or
fallacies in whatever order takes one's fancy.
The first three chapters are largely concerned with examples that
today are generally classed as fallacies. As such, they have specific
defects in the mathematics, defects upon which all mathematicians
are in agreement.
It seems appropriate to encourage the reader to try finding those
defects. Therefore, I stop at a point where the presentation of the
fallacy is complete and ask: Can You Find the Flaw? I also provide
a hint. The remaining chapters deal with topics for which there is no
single, accepted explanation, so this feature is dropped in Chapters
4 through 8.
I assume throughout that the reader has some experience with the
content of first-year high-school algebra. A few of the results also
draw upon parts of high-school geometry. Any mathematics that is
needed beyond these levels is developed as a topic in the body of the
book. This includes a brief introduction to the basic ideas of complex
numbers in Chapter I; mathematical indu~tion, the notion of
the limit of a series, and some ideas from probability in Chapter 2;
indirect proof in Chapter 3; and elementary set theory in Chapter
5. These are all necessary to a complete understanding of many of
the paradoxes. Even so, there are some mathematical complexities
that I have omitted deliberately. For example, the discussion of
Godel's incompleteness theorem is necessarily simplified (even the
type of incompleteness to which it applies is omitted), as is the
analysis of special relativity. These simplifications in no way affect
the results stated. In a few cases, it has seemed better to state results
without proof, rather than to become bogged down in lengthy and
difficult mathematical development.
I wish to express my gratitude to Dr. Phillip S. Jones of the University
of Michigan for his thoughtful comments on much of the material
in the manuscript; and to my wife, Mary, for retyping the whole
manuscript, as well as for her help and support in so many other
ways.
Briarcliff Manor, NY
B.H.B.

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