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The Mathematics of Infinity: A Guide to Great Ideas Book

The Mathematics of Infinity: A Guide to Great Ideas
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The Mathematics of Infinity: A Guide to Great Ideas, Praise for the First Edition . . . an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity.—Computing Reviews . . . a very well written introduction to set theory . . . easy to read and, The Mathematics of Infinity: A Guide to Great Ideas
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  • The Mathematics of Infinity: A Guide to Great Ideas
  • Written by author Theodore G. Faticoni
  • Published by Wiley, John & Sons, Incorporated, 4/10/2012
  • Praise for the First Edition ". . . an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity."—Computing Reviews ". . . a very well written introduction to set theory . . . easy to read and
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Book Categories

Authors

1. Logic 1

1.1 Axiomatic Method 2

1.2 Tabular Logic 3

1.3 Tautology 9

1.4 Logical Strategies 15

1.5 Implications From Implications 17

1.6 Universal Quantifiers 20

1.7 Fun With Language and Logic 22

2. Sets 29

2.1 Elements and Predicates 30

2.2 Cartesian Products 45

2.3 Power Sets 48

2.4 Something From Nothing 50

2.5 Indexed Families of Sets 56

3. Functions 65

3.1 Functional Preliminaries 66

3.2 Images and Preimages 81

3.3 One-to-One and Onto Functions 90

3.4 Bijections 95

3.5 Inverse Functions 97

4. Counting Infinite Sets 105

4.1 Finite Sets 105

4.2 Hilbert’s Infinite Hotel 113

4.3 Equivalent Sets and Cardinality 128

5. Infinite Cardinals 135

5.1 Countable Sets 136

5.2 Uncountable Sets 149

5.3 Two Infinites 159

5.4 Power Sets 166

5.5 The Arithmetic of Cardinals 180

6. Well Ordered Sets 199

6.1 Successors of Elements 199

6.2 The Arithmetic of Ordinals 210

6.3 Cardinals as Ordinals 222

6.4 Magnitude versus Cardinality 234

7. Inductions and Numbers 243

7.1 Mathematical Induction 243

7.2 Sums of Powers of Integers 260

7.3 Transfinite Induction 264

7.4 Mathematical Recursion 274

  7.5 Number Theory 279

7.6 The Fundamental Theorem of Arithmetic 283

7.7 Perfect Numbers 285

8. Prime Numbers 289

8.1 Prime Number Generators 289

8.2 The Prime Number Theorem 292

8.3 Products of Geometric Series 296

8.4 The Riemann Zeta Function 302

8.5 Real Numbers 307

9. Logic and Meta-Mathematics 313

9.1 The Collection of All Sets 313

9.2 Other Than True or False 317

9.3 Logical Implications of A Theory of Everything 326

Bibliography 283

Index 284 


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The Mathematics of Infinity: A Guide to Great Ideas, Praise for the First Edition
. . . an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity.—Computing Reviews
. . . a very well written introduction to set theory . . . easy to read and, The Mathematics of Infinity: A Guide to Great Ideas

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The Mathematics of Infinity: A Guide to Great Ideas, Praise for the First Edition
. . . an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity.—Computing Reviews
. . . a very well written introduction to set theory . . . easy to read and, The Mathematics of Infinity: A Guide to Great Ideas

The Mathematics of Infinity: A Guide to Great Ideas

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The Mathematics of Infinity: A Guide to Great Ideas, Praise for the First Edition
. . . an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity.—Computing Reviews
. . . a very well written introduction to set theory . . . easy to read and, The Mathematics of Infinity: A Guide to Great Ideas

The Mathematics of Infinity: A Guide to Great Ideas

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