The Mathematics of Infinity —— A Guide to Great Ideas

----- 无穷的数学：伟大的思想指南，第2版

ISBN: 9781118204481 出版年：2012 页码：360 Theodore G Faticoni Wiley

Preface. 1. Elementary Set Theory. 1.1 Sets. 1.2 Cartesian Products. 1.3 Power Sets. 1.4 Something From Nothing. 1.5 Indexed Families of Sets. 2. Functions. 2.1 Functional Preliminaries. 2.2 Images and Preimages. 2.3 One-to-one and Onto . 2.4 Bijections. 2.5 Inverse Functions. 3. Counting Infinite Sets. 3.1 Finite Sets. 3.2 Hilbert's Infinite Hotel. 3.3 Equivalent Sets and Cardinality. 4. Infinite Cardinals. 4.1 Countable Sets. 4.2 Uncountable Sets. 4.3 Two Infinities. 4.4 Power Sets. 4.5 The Arithmetic of Cardinals. 5. Well Ordered Sets. 5.1 Successors of Elements. 5.2 The Arithmetic of Ordinals. 5.4 Magnitude versus Cardinality. 6. Inductions and Numbers. 6.1 Mathematical Induction. 6.2 Transfinite Induction. 6.3 Mathematical Recursion . 6.4 Number Theory. 6.5 The Fundamental Theorem of Arithmetic. 6.6 Perfect Numbers. 7. Prime Numbers. 7.1 Prime Number Generators. 7.2 The Prime Number Theorem. 7.3 Products of Geometric Series. 7.4 The Riernann Zeta Function. 7.5 Real Numbers. 8. Logic and Meta-Mathematics. 8.1 The Collection of All Sets. 8.2 Other Than True or False. Bibliography. Index.