The mathematics of infinity : a guide to great ideas / Theodore G. Faticoni.

Format:

Book

Author/Creator:

Faticoni, Theodore G. (Theodore Gerard), 1954-

Series:

Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts

Pure and applied mathematics

Language:

English

Subjects (All):

Cardinal numbers.

Infinite.

Set theory.

Physical Description:

1 online resource (360 p.)

Edition:

2nd ed.

Place of Publication:

Hoboken, N.J. : John Wiley & Sons, c2012.

Language Note:

English

System Details:

text file

Summary:

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 well suited for self-study . . . highly recommended.""-Choice The concept of infinity has fascinated and confused mankind for centuries with theories and ideas that cause even seasoned mathematicians to wonder. The Mathematics of Infinity: A Guide to Great Ideas, Second Edition uniquely explores how we can manipulate these idea

Contents:

The Mathematics of Infinity: A Guide to Great Ideas; Contents; Preface for the Second Edition; 1 Logic; 1.1 Axiomatic Method; 1.2 Tabular Logic; 1.3 Tautology; 1.4 Logical Strategies; 1.5 Implications From Implications; 1.6 Universal Quantifiers; 1.7 Fun With Language and Logic; 2 Sets; 2.1 Elements and Predicates; 2.2 Equality; 2.3 Cartesian Products; 2.4 Power Sets; 2.5 Something From Nothing; 2.6 Indexed Families of Sets; 3 Functions; 3.1 Functional Preliminaries; 3.2 Images and Preimages; 3.3 One-to-One and Onto Functions; 3.4 Bijections; 3.5 Inverse Functions; 4 Counting Infinite Sets

4.1 Finite Sets 4.2 Hilbert's Infinite Hotel; 4.3 Equivalent Sets and Cardinality; 5 Infinite Cardinals; 5.1 Countable Sets; 5.2 Uncountable Sets; 5.3 Two Infinities; 5.4 Power Sets; 5.5 The Arithmetic of Cardinals; 6 Well-Ordered Sets; 6.1 Successors of Elements; 6.2 Constructing Well Ordered Sets; 6.3 Cardinals as Ordinals; 6.4 Magnitude versus Cardinality; 7 Inductions and Numbers; 7.1 Mathematical Induction; 7.2 Sums of Powers of Integers; 7.3 Transfinite Induction; 7.4 Mathematical Recursion; 7.5 Number Theory; 7.6 The Fundamental Theorem of Arithmetic; 7.7 Perfect Numbers

8 Prime Numbers 8.1 Prime Number Generators; 8.2 The Prime Number Theorem; 8.3 Products of Geometric Series; 8.4 The Riemann Zeta Function; 8.5 Real Numbers; 9 Logic and Meta-Mathematics; 9.1 The Collection of All Sets; 9.2 Other Than True or False; 9.3 The Logic of A Theory of Everything; 9.3.1 Gödel's Incompleteness Theorem; 9.3.2 Logically Closed Sets; 9.3.3 Applications; Bibliography; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786613622389

9781280592553

1280592559

9781118243855

1118243854

9781118243879

1118243870

9781118243824

111824382X

OCLC:

795795376