The Mathematics of Infinity

Praise for the First Edition
". . . an enchanting book for those people in computer scienceor mathematics who are fascinated by the concept ofinfinity."--Computing Reviews
". . . a very well written introduction to set theory . . . easyto read and well suited for self-study . . . highlyrecommended."--Choice
The concept of infinity has fascinated and confused mankind forcenturies with theories and ideas that cause even seasonedmathematicians to wonder. The Mathematics of Infinity: A Guide toGreat Ideas, Second Edition uniquely explores how we can manipulatethese ideas when our common sense rebels at the conclusions we aredrawing.
Continuing to draw from his extensive work on the subject, theauthor provides a user-friendly presentation that avoidsunnecessary, in-depth mathematical rigor. This Second Editionprovides important coverage of logic and sets, elements andpredicates, cardinals as ordinals, and mathematical physics.Classic arguments and illustrative examples are provided throughoutthe book and are accompanied by a gradual progression ofsophisticated notions designed to stun readers' intuitive view ofthe world.
With an accessible and balanced treatment of both concepts andtheory, 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, TheMathematics of Infinity: A Guide to Great Ideas, Second Edition isan insightful supplement for mathematics courses on set theory atthe undergraduate level. The book also serves as a fascinatingreference for mathematically inclined individuals who areinterested in learning about the world of counterintuitivemathematics.