Pub. Date:
Facts on File, Incorporated
Numbers: Computers, Philosophers, and the Search for Meaning

Numbers: Computers, Philosophers, and the Search for Meaning

by John Tabak


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Product Details

ISBN-13: 9780816049554
Publisher: Facts on File, Incorporated
Publication date: 06/28/2004
Series: Facts on File Math Library
Pages: 240
Product dimensions: 6.10(w) x 9.20(h) x 0.80(d)
Age Range: 11 - 17 Years

Table of Contents

Introduction: Number and Imaginationxi
Part 1Numbers for Computation1
1The First Problems3
2Early Counting Systems11
A Mesopotamian Education13
The Mesopotamian Number System14
Mesopotamian Mathematics Homework18
The Egyptian Number System20
A Problem from the Ahmes Papyrus24
The Mayan Number System26
The Chinese Number System30
A Problem from the Nine Chapters32
3Our Place Value Number System34
Explaining the New System38
4Analytical Engines46
Calculators, Computers, and the Human Imagination48
Charles Babbage and the Analytical Engine50
An Early Electronic Representation of Our Number System52
Floating-Point Representation56
Floating-Point Arithmetic and Your Calculator58
Why Computers?60
Part 2Extending the Idea of a Number65
5An Evolving Concept of a Number67
Irrational Numbers70
Pythagoras of Samos73
The Irrationality of [radical]275
6Negative Numbers77
Ancient Mathematical Texts from the Indian Subcontinent82
Out of India83
7Algebraic Numbers85
Tartaglia, Ferrari, and Cardano88
Girard and Wallis93
Euler and d'Alembert97
The Debate over "Fictitious" Numbers98
The Complex Numbers: A Modern View103
Using Complex Numbers104
8Transcendental Numbers and the Search for Meaning107
Dedekind and the Real Number Line111
Part 3The Problem of Infinity117
9Early Insights119
10Galileo and Bolzano130
Infinity as a Number136
The Life and Opinions of Tristram Shandy, Gentleman140
11Georg Cantor and the Logic of the Infinite143
There Are No More Rational Numbers than Natural Numbers146
There Are More Real Numbers than Natural Numbers148
The Russell Paradox154
Resolving the Russell Paradox159
12Cantor's Legacy165
Kurt Godel170
Formal Languages Today173
Alan Turing174
Further Reading203

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