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Philosophy of Numbers

Philosophy of Numbers

Specifications

Item Code: IDI811

by Jayant Burde

Hardcover (Edition: 2007)

Munshiram Manoharlal Publishers Pvt. Ltd.
ISBN 8121511763

Size: 8.8" X 5.6
Pages: 262
Price: $40.00   Shipping Free
Viewed times since 2nd Oct, 2008

Description

From The Jacket

This book is about numbers and so many questions relating to them. What is the nature of numbers are they discovered or invented? What is mystical about them? Mathematicians develop a hierarchy of numbers in which mysterious dichotomies appear. For example, the integer 5 is not the same as the rational 5 which in turn is different from the real 5. The author explains how this conceptual maze does not affect the laypersons' arithmetic. He also discusses such fascinating topics as primes, perfect numbers, inaccessible numbers and many other unsolved problems relating to the treacherous terrain of infinity, which have baffled mathematicians and philosophers alike.

Jayant Burde has academic/professional qualifications in mathematics, physics, haw and banking. His published papers contain mathematical models in finance and organizational structure. He is also the author of the book Rituals, Mantras and Science.

Preface

This book is about numbers. It tries to answer many questions relating to them. What is the nature of number? Are they discovered or invented? Are they eternal or immortal? What are finite and infinite numbers? What is mystical about them?

It shows, how starting with a collection of objects a hierarchy of numbers-the natural numbers, integers, rationals, irrationals, real numbers and complex numbers can be constructed. It also discusses such topics as primes, perfect numbers, infinite numbers, cryptopgraphy, Fibonacci numbers, the Fermat's last theorem and also many unsolved problems relating to numbers.

The only prerequisite for understanding this book is the knowledge of high school mathematics and a desire to know more about numbers. All mathematical concepts which the common reader is not likely to be familiar are explained at the appropriate stages. Since this is not a treatise on mathematics most theorems are stated without proof.

Most of these results can be appreciated intuitively except those which baffle even mathematicians. I hope, the many illustrations which I have included will enable the reader to have an insight which a rigorous formal treatment cannot provide.

Though meant for a general audience, the students of mathematics and philosophy should also find the book interesting. Bertrand Russell often reprimanded philosophers for not learning sufficient mathematics. A similar criticism can be leveled against mathematicians who feel that philosophy is either irrelevant or far beneath their intellectual level.

With their superior logical mind mathematicians can create countless systems which are self-consistent. Most of these systems are, however, drab unless they have a philosophical dimensions. If mathematicians care to develop a philosophical approach to their problems, they will find a new depth which will enable them to unify and solve many problems which appear disparate as well as intractable. What's more, they will find, to their surprise, tha philosophy can provide a link between their abstruse world of symbols and the world in which common people live.

There are a few books on the philosophy of mathematics, but I have not come across a treatise which exclusively deals with numbers. I hope this book will fill this void.

Prefaceix
Acknowledgementsxi
1The Numbers We Know1
2The Natural Numbers-The Serial Concept10
3Sets and Classes14
4The Algebra of Sets21
5Relations27
6The Natural Numbers and Logic35
7Mapping42
8The Natural Numbers and Mapping50
9Abstract Algebra56
10Order66
11Finite and Infinite Numbers72
12Relation Number and Structure79
13The Integers and Rationals as Relations83
14The Integers as Classes87
15Rational Numbers as Classes94
16Real Numbers-Dedekind's Theory98
17Sequences103
18The Real Numbers110
19The Real Numbers and Infinite Continuum119
20The Complex Numbers128
21Infinite Cardinals and Ordinals135
22The Elusive Primes143
23Numbers and Secret Communications152
24The Mystical Perfect Numbers163
25The Fermat's Last Theorem171
26Some Intriguing Numbers180
27The Grammar of Numbers187
28The Treacherous Infinity199
29Wrestling with Numbers207
30Numbers: Reality and Mysticism222
31The Nature of Numbers233
Bibliography247
Index249
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