Contributions to the founding of the theory of transfinite numbers. Translated, and provided with an introd. and notes, by Philip E. B. Jourdain

Cantor, Georg

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ISBN 10: 0486600459 ISBN 13: 9780486600451

Published by Dover [1955], New York, 1955

Language: English

Condition: Used - Very good Soft cover

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Bibliographic Details

Title

Contributions to the founding of the theory of transfinite numbers. Translated, and provided with an introd. and notes, by Philip E. B. Jourdain

Publisher

Dover [1955], New York

Publication Date

1955

Language

English

ISBN 10

0486600459

ISBN 13

9780486600451

Binding

Paperback

Edition

later printing.

Condition

Very good condition

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Science & Technology

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Synopsis

One of the greatest mathematical classics of all time, this work established a new field of mathematics which was to be of incalculable importance in topology, number theory, analysis, theory of functions, etc., as well as in the entire field of modern logic. It is rare that a theory of such fundamental mathematical importance is expressed so simply and clearly: the reader with a good grasp of college mathematics will be able to understand most of the basic ideas and many of the proofs.
Cantor first develops the elementary definitions and operations of cardinal and ordinal numbers and analyzes the concepts of "canlinality" and "ordinality." He covers such topics as the addition, multiplication, and exponentiation of cardinal numbers, the smallest transfinite cardinal number, the ordinal types of simply ordered aggregates, operations on ordinal types, the ordinal type of the linear continuum, and others. He then develops a theory of well-ordered aggregates, and investigates the ordinal numbers of well-ordered aggregates and the properties and extent of the transfinite ordinal numbers.
An 82-page introduction by the eminent mathematical historian Philip E. B. Jourdain first sketches the background of Cantor's theory, discussing the contributions of such predecessors as Veicrstrass, Cauchy, Dedekind, Dirichlet, Riemann, Fourier, and Hankel; it then traces the development of the theory by summarizing and analyzing Cantor's earlier work. A bibliographical note provides information on further investigations in the theory of transfinite numbers by Frege, Peano, Whitehead, Russell, etc.
"Would serve as well as any modern textto initiate a student in this exciting branch of mathematics." — Mathematical Gazette.

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James Lawton, a graduate of Benedictine University, has Master?s degrees in English and in Library Science from the University of Michigan. From 1963 to 1967, he served as the Rare Book Assistant for the Department of Rare Books and Special Collections, at the University of Michigan. He was the Rare Book Bibliographer at Syracuse University Library, in 1967 and 1968. In 1969 he was appointed Curator of Manuscripts, Department of Rare Books and Manuscripts, Boston Public Library. He became Assistant Keeper of Rare Books and Manuscripts Boston Public Library, in 1975. From 1980 to 2000 he was the owner and proprietor of Brookline Village Books, a retail establishment specializing in general out-of-print, scholarly, and rare books. In 2000 the business became internet based only under the name J. Lawton, Booksellers.

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