In Search of Infinity

In Search of Infinity

by N.Ya. Vilenkin
     
 

The concept of infinity is one of the most important, and at the same time, one of the most mysterious concepts of science. Already in antiquity many philosophers and mathematicians pondered over its contradictory nature. In mathematics, the contradictions connected with infinity intensified after the creation, at the end of the 19th century, of the theory of

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Overview

The concept of infinity is one of the most important, and at the same time, one of the most mysterious concepts of science. Already in antiquity many philosophers and mathematicians pondered over its contradictory nature. In mathematics, the contradictions connected with infinity intensified after the creation, at the end of the 19th century, of the theory of infinite sets and the subsequent discovery, soon after, of paradoxes in this theory. At the time, many scientists ignored the paradoxes and used set theory extensively in their work, while others subjected set-theoretic methods in mathematics to harsh criticism. The debate intensified when a group of French mathematicians, who wrote under the pseudonym of Nicolas Bourbaki, tried to erect the whole edifice of mathematics on the single notion of a set. Some mathematicians greeted this attempt enthusiastically while others regarded it as an unnecessary formalization, an attempt to tear mathematics away from life-giving practical applications that sustain it. These differences notwithstanding, Bourbaki has had a significant influence on the evolution of mathematics in the twentieth century. In this book we try to tell the reader how the idea of the infinite arose and developed in physics and in mathematics, how the theory of infinite sets was constructed, what paradoxes it has led to, what significant efforts have been made to eliminate the resulting contradictions, and what routes scientists are trying to find that would provide a way out of the many difficulties.

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Editorial Reviews

From the Publisher
"In fewer than 150 pages Vilenkin has packed a whole course on infinity: its history, philosophy, and mathematical theory. Abe Shenitzer's translation is very smooth and natural... When fractals have gone out of style, and chaos is no longer the flavor of the month, some kind of 'geometric set theory' or 'set-theoretic geometry' may very well remain, and In Search of Infinity may still be the best introduction to it."

—American Mathematical Monthly

Booknews
For non-specialists and lay readers comfortable with mathematical thinking, outlines the importance of infinity in human thought since records began, then traces efforts since the 19th century to understand and represent infinity in mathematics and physics. Primarily concerned with the paradoxes generated by the theory of infinite sets that lie at the heart of most mathematics, and the intellectual writhing to come to terms with them. Translated from the second Russian edition of V poiskakh beskonechnosti, which was first published about 20 years ago. No index. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Product Details

ISBN-13:
9781461269151
Publisher:
Birkhauser Verlag
Publication date:
06/28/2013
Edition description:
Softcover reprint of the original 1st ed. 1995
Pages:
146
Product dimensions:
6.14(w) x 9.21(h) x 0.33(d)

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