The Mathematics of Infinity: A Guide to Great Ideas

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John Wiley & Sons, Jul 6, 2006 - Mathematics - 320 pages
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A balanced and clearly explained treatment of infinity in mathematics.

The concept of infinity has fascinated and confused mankind for centuries with concepts and ideas that cause even seasoned mathematicians to wonder. For instance, the idea that a set is infinite if it is not a finite set is an elementary concept that jolts our common sense and imagination. the Mathematics of Infinity: A guide to Great Ideas uniquely explores how we can manipulate these ideas when our common sense rebels at the conclusions we are drawing.

Writing with clear knowledge and affection for the subject, the author introduces and explores infinite sets, infinite cardinals, and ordinals, thus challenging the readers' intuitive beliefs about infinity. Requiring little mathematical training and a healthy curiosity, the book presents a user-friendly approach to ideas involving the infinite. readers will discover the main ideas of infinite cardinals and ordinal numbers without experiencing in-depth mathematical rigor. Classic arguments and illustrative examples are provided throughout the book and are accompanied by a gradual progression of sophisticated notions designed to stun your intuitive view of the world.

With a thoughtful and balanced treatment of both concepts and theory, The Mathematics of Infinity focuses on the following topics:
* Sets and Functions
* Images and Preimages of Functions
* Hilbert's Infinite Hotel
* Cardinals and Ordinals
* The Arithmetic of Cardinals and Ordinals
* the Continuum Hypothesis
* Elementary Number Theory
* The Riemann Hypothesis
* The Logic of Paradoxes

Recommended as recreational reading for the mathematically inquisitive or as supplemental reading for curious college students, the Mathematics of Infinity: A Guide to Great Ideas gently leads readers into the world of counterintuitive mathematics.
  

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User Review - Flag as inappropriate

There are several math errors in the book that clearly not typos. For example on page 61 he states that the mass of the earth is about 10^100 grams. It is actually about 6*10^30 grams.

Review: The Mathematics of Infinity: A Guide to Great Ideas

User Review  - Peter Mcloughlin - Goodreads

A fun book I saw a lot of the material before but some stuff was new to me. It can be understood by someone who did really well in High School Math. It would take some effort but it is rewarding. Read full review

Contents

1 Elementary Set Theory
1
2 Functions
37
3 Counting Infinite Sets
75
4 Infinite Cardinals
103
5 Well Ordered Sets
163
6 Inductions and Numbers
205
7 Prime Numbers
247
8 Logic and MetaMathematics
271
Bibliography
283
Index
284
Copyright

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About the author (2006)

Theodore G. Faticoni, PhD, is Professor in the Dept. of Mathematics at Fordham University.† He received his PhD in Mathematics from the Univ. of Connecticut in 1981.† His professional experience includes 30 research papers in peer reviewed journals and 30 lectures on his research to his colleagues.

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