The Mathematics of Infinity / Wiley Series in Pure and Applied Mathematics (PDF)

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.