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

4.8 out of 5 stars 12 customer reviews

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Editorial Reviews

Review

Praise for Lillian Lieber and Infinity

"The interpolations tying mathematics into human life and thought are brilliantly clear."—Booklist

"Her presentation…is conversational and humorous, and should help to simplify some complex concepts."—Kirkus

"Another excellent book for the lay reader of mathematics…In explaining [infinity], the author introduces the reader to a good many other mathematical terms and concepts that seem unintelligible in a formal text but are much less formidable when presented in the author's individual and very readable style."—Library Journal

"Mrs. Lieber, in this text illustrated by her husband, Hugh Gray Lieber, has tackled the formidable task of explaining infinity in simple terms, in short line, short sentence technique popularized by her in The Education of T.C. MITS."—Chicago Sunday Tribune

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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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: 5 x 0.7 x 8 inches
  • Shipping Weight: 8.8 ounces (View shipping rates and policies)
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (12 customer reviews)
  • Amazon Best Sellers Rank: #1,002,125 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

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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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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By A Customer 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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Format: Paperback Verified Purchase
I first read this book 5 years ago, but now I have just have been reading it once again, and I again find the book to be fine by its easy understandable text, and the many drawings, by which trying to show geometrical and speculatively how to look, and think, about the Infinitive. And thereby being helpful especially to persons who during self-study are trying to learn about the mathematical behind the Infinity which Cantor proved, and how Cantor probably was speculating when he came to these ideas and conclusions.

But if it come to having more reading about the Infinity with even les mathematic (But personally I like heavy mathematic and formulas), then I will recommend these books: Amir D. Aczel: "The Mystery of the Aleph, Mathematics, the Kabbalah, and the Search for Infinity", and Eli Maor: "To Infinity and Beyond, A Cultural History of the Infinity". But if interested in much mathematic and geometry (much parallel to how we are watching it used in fractals) then we for example have a 152 sides, A5, book, written by Leo Zippin: "Uses of Infinity", first printed in 1962, and mine, from Dover, in 2000.

But now a day we in many books are reading about the Infinity, especially since we around 90 years ago started reading, thinking, and speculating about the Infinity of parallel Universes.
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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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Format: Paperback Verified Purchase
Explains a difficult and strange subject clearly and is amplified by associated and delightful drawings that illustrate and translate the mathematical points into artistic impression. The authors proceed slowly, step by step, and the work does not require advanced mathematical knowledge, just the ability to open the mind to different and new ways of understanding concepts.
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