The Mathematics of Infinity: A Guide to Great Ideas

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John Wiley & Sons, Apr 17, 2012 - Mathematics - 338 pages
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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 ideas when our common sense rebels at the conclusions we are drawing.

Continuing to draw from his extensive work on the subject, the author provides a user-friendly presentation that avoids unnecessary, in-depth mathematical rigor. This Second Edition provides important coverage of logic and sets, elements and predicates, cardinals as ordinals, and mathematical physics. Classic arguments and illustrative examples are provided throughout the book and are accompanied by a gradual progression of sophisticated notions designed to stun readers' intuitive view of the world.

With an accessible and balanced treatment of both concepts and theory, the book focuses on the following topics:

  • Logic, sets, and functions

  • Prime numbers

  • Counting infinite sets

  • Well ordered sets

  • Infinite cardinals

  • Logic and meta-mathematics

  • Inductions and numbers

Presenting an intriguing account of the notions of infinity, The Mathematics of Infinity: A Guide to Great Ideas, Second Edition is an insightful supplement for mathematics courses on set theory at the undergraduate level. The book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the world of counterintuitive mathematics.

 

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Contents

Logic
1
Sets
29
Functions
67
Counting Infinite Sets
107
Infinite Cardinals
137
WellOrdered Sets
201
Inductions and Numbers
245
Prime Numbers
291
Logic and MetaMathematics
315
Bibliography
333
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About the author (2012)

THEODORE G. FATICONI, PhD, is a Professor in the Department of Mathematics at Fordham University. His professional experience includes forty research papers in peer-reviewed journals and forty lectures on his research to his colleagues.

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