Contributions to the Founding of the Theory of Transfinite Numbers (Dover Books on MaTHEMA 1.4tics)

Cantor, Georg

ISBN 10: 0486600459 / ISBN 13: 9780486600451

Published by Dover Publications Inc, 2003

About this Item

Photos included in listing. About the book: 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 text to initiate a student in this exciting branch of mathematics." Mathematical Gazette.

Seller Inventory # 1375

Bibliographic Details

• Title: Contributions to the Founding of the Theory of Transfinite Numbers (Dover Books on MaTHEMA 1.4tics)
• Publisher: Dover Publications Inc
• Publication Date: 2003
• Language: English
• ISBN 10: 0486600459
• ISBN 13: 9780486600451
• Binding: Soft cover
• Edition: 1st Edition
• Condition: Very Good
• Weight: 250 grams
• Seller catalogs:
  • Mathematics

About this title

Synopsis

The famous articles, 1895–7, that founded a new branch of mathematics.
Covers addition, multiplication and exponentiation of cardinal numbers, smallest transfinite cardinal numbers, ordinal types of simple ordered aggregates and operations on ordinal types. Develops theory of well-ordered aggregates; investigates ordinal numbers of well-ordered aggregates and more.
Translated with introduction by P. Jourdain.

From the Back Cover

"In it, Jourdain outlines the contributions of many of Cantor's forerunners--including Fourier, Dirichlet, Cauchy, Weierstrass, Riemann, Dedekind, and Hankel--and then further contextualizes Cantor's groundbreaking theory by recounting and examining his earlier work. In this volume, Cantor addresses: -the addition and multiplication of powers, -the exponentiation of powers, -the finite cardinal numbers, -the smallest transfinite cardinal number aleph-zero, -addition and multiplication of ordinal types -well-ordered aggregates the ordinal numbers of well-ordered aggregates, -and much more. German mathematician GEORG CANTOR (1845-1918) is best remembered for formulating set theory. His work was considered controversial at the time, but today he is widely recognized for his important contributions to the field of mathematics."