Contributions to the Founding of the Theory of Transfinite Numbers

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Courier Corporation, 1952 - Mathematics - 211 pages
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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.

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User Review  - Landric - LibraryThing

As a teenager studying mathematics, I was fascinated by Cantor's notion of an infinity of infinities. Then I bought this book and read the arguments behind his theories, and realized that, although he ... Read full review

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Remarquable, acheter d'urgence !!!!

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About the author (1952)

Georg Cantor was born in St. Petersburg, Russia, in 1845, but was educated and lived the rest of his life in Germany. He studied in Berlin and became a professor of mathematics in 1877. He was the creator of set theory and the founder of the theory of transfinite numbers. Cantor's most important work appeared between 1895 and 1897. In addition to developing the philosophical implications of his transfinite set theory, Cantor also studied the theological implications of his work. He founded the German Mathematicians Union in 1891 and served as its first president. It has been said that Cantor became mentally unstable in later life because the mathematics community did not immediately accept his work.

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