Infinity: Beyond the Beyond the Beyond

Front Cover
Paul Dry Books, 1953 - Mathematics - 262 pages
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"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

Infinity. It sounds simple…but is it? This elegant, accessible, and playful book artfully illuminates one of the most intriguing ideas in mathematics. Lillian Lieber presents an entertaining, yet thorough, explanation of the concept and cleverly connects mathematical reasoning to larger issues in society.Infinity includes a new foreword by Harvard professor Barry Mazur.

"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

 

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Contents

Dedication
13
Infinity in Mathematics
27
More About Potential Infinity
40
NonEuclidean Geometries
62
Actual Infinity
77
Actual Infinity cont
87
A Still Greater Actual Infinity
100
The Continuum of Real Numbers
109
Operations on Transfinites 13 7
137
Higher Dimensions
147
A Hierarchy of Infinities
161
A Brief Summary
182
Is It Legitimate?
194
Some Very Interesting Infinite Sets
204
Paradoxes in the Theory ofTransfinites
240
The Moral
257

How To Go from 80 to c
125

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About the author (1953)

Lillian Lieber was the head of the Department of Mathematics at Long Island University. She wrote a series of lighthearted (and well-respected) math books in the 1940s, including The Einstein Theory of Relativity and The Education of T.C. MITS (also published by Paul Dry Books).

Hugh Gray Lieber was the head of the Department of Fine Arts at Long Island University. He illustrated many books written by his wife Lillian.

Barry Mazur is a mathematician and is the Gerhard Gade University Professor at Harvard University. He is the author of Imagining Numbers (particularly the square root of minus fifteen). He has won numerous honors in his field, including the Veblen Prize, Cole Prize, Steele Prize, and Chauvenet Prize.

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