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Infinity: Beyond the Beyond the Beyond Paperback – November 1, 2007


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Infinity: Beyond the Beyond the Beyond + The Einstein Theory of Relativity: A Trip to the Fourth Dimension + The Education of T.C. Mits: What modern mathematics means to you
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Product Details

  • Paperback: 359 pages
  • Publisher: Paul Dry Books; 1st Paul Dry Books Ed edition (November 1, 2007)
  • Language: English
  • ISBN-10: 1589880366
  • ISBN-13: 978-1589880368
  • Product Dimensions: 0.6 x 5.4 x 7.8 inches
  • Shipping Weight: 8.8 ounces (View shipping rates and policies)
  • Average Customer Review: 4.9 out of 5 stars  See all reviews (9 customer reviews)
  • Amazon Best Sellers Rank: #910,434 in Books (See Top 100 in Books)

Editorial Reviews

About the Author

Lillian R. Lieber was Professor and Head of the Department of Mathematics at Long Island University. She wrote a series of light-hearted (and well-respected) math books, many of them illustrated by her husband. Hugh Gray Lieber was Professor and Head of the Department of Fine Arts at Long Island University. Barry Mazur does his mathematics at Harvard University and lives in Cambridge, Massachussetts, with the writer Grace Dane Mazur. He is the author of "Imagining Numbers (Particularly the Square Root of Minus Fifteen)" (FSG, 2003). He has won numerous prizes in his field, including the Veblen Prize, Cole Prize, Steele Prize, and Chauvenet Prize.

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Customer Reviews

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Most Helpful Customer Reviews

18 of 18 people found the following review helpful By Dawson C. Smith on August 24, 2008
Format: Paperback Verified Purchase
Nobody explains mathematical ideas for the layman as does Lillian R. Lieber. And the fanciful illustrations that always accompany her work, done by Hugh Gray Lieber, are amusing and informative.

Infinity: Beyond the Beyond the Beyond presents an account of how mathematics has learned to deal with the infinite, primarily through the work of Georg Cantor. Controversial at first, Cantor's set theory and transfinite arithmetic are now part of the foundations of modern mathematics. Perhaps the most startling idea to be had from this book is that infinite sets are not all the same size.

I have before me a copy of the 1953 original, as well as the 2007 abridgement. Aside from the fact that the older book is a hardcover, the abridgement is the better book. The editor, Barry Mazur, a mathematician at Harvard, has removed the dated, nonmathematical introductory material and the chapters on calculus. This book is now a superb layman's guide to the mathematics of transfinities.

If you would like more biography and less mathematics, you might try The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity, by Amir D. Aczel. And two magazine articles are worth seeking out: "Georg Cantor and the Origins of Transfinite Set Theory," by Joseph W. Dauben, Scientific American, June 1983; and "Non-Cantorian Set Theory," by Paul J. Cohen and Reuben Hersh, Scientific American, December 1967.

Note: In 1900, David Hilbert put forth a list of the 23 most important unsolved problems in mathematics. At the head of the list was Cantor's continuum hypothesis. The problem was still open when the Liebers wrote their book.
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10 of 10 people found the following review helpful By Brian Marley on November 26, 2003
Format: Hardcover
This is a great book. I first found it in my high school library. For the uninitiated, who would have thought there were different levels of infinity? This book explains infinity in a readable and entertaining way. It is too bad this book is out of print as I suspect it would still be in high demand. It would make a great title for a book club. Somebody needs to republish it!
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16 of 18 people found the following review helpful By "maguszero" on May 30, 2001
Format: Hardcover
Lillian Lieber and her husband Hugh created some of the most wonderful books in the fields of mathematics, logic, and relativity. Although some of my fondest childhood memories are the hours I spent trying to fully grasp the meaning in her books, I find these same books to be no less enjoyable today as an adult. I cannot recommend her books highly enough.
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9 of 11 people found the following review helpful By A guy named Joe on February 21, 2002
Format: Hardcover
As an Army brat, I found this book in the school library on the Naval base in Tianan, Tiawan in 1958.
As a 10th grader with a fondness for math, it was great. I think I'd seen a little bit about transfinite numbers in George Gamow's "1 2 3 Infinity", but this was an amazing tour of transfinite numbers, written so it could be understood by T C Mits. I learned a lot from it -- a real mind stretcher. I later recognized other books by the same author by the illustrations -- If you know her other books, nothing more need be said.
I've not seen the book in over 40 years, but decided I needed to find a copy -- it's one of the favorite books I read before college. I was looking at my copy of "The Education of T.C.Mits" and decided to see what I could find.
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10 of 13 people found the following review helpful By Triumfer on July 6, 2008
Format: Paperback
Beware! This is not Lillian Lieber's original work. It has been abridged. Approximately one third of the original text and presumably the drawings have disappeared. In the forward, Barry Mazur, states plainly that he zapped Lillian's preface, chapter 1, one half of chapter 17, and all of chapters 18 through to 24. Gone is Lillian's introduction to SAM, Lillian's spirit creature of Science, Art, and Mathematics. Why did Mazur do this? He thought the Liebers digressed too much. He wanted them to stay on track with the main subject, transfinite mathematics. He thought that some of their worldly concerns speak less to a modern audience than they did to their readers in 1953. However we have to take Dr. Mazur's word for it, as the sections are deleted and you can no longer judge for yourself. Despite my misgivings I give a 5 star rating as what is left is still beautiful. However you may wish to try the used book market to get the original version.
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