Contributions to the Founding of the Theory of Transfinite Numbers (Dover Books on Mathematics)

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9780486600451: Contributions to the Founding of the Theory of Transfinite Numbers (Dover Books on Mathematics)

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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Cantor, Georg
Editorial: Dover Publishers
ISBN 10: 0486600459 ISBN 13: 9780486600451
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Descripción Dover Publishers. Estado de conservación: New. Brand New. Nº de ref. de la librería 0486600459

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Georg Cantor
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ISBN 10: 0486600459 ISBN 13: 9780486600451
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Descripción Dover Publications Inc., United States, 1955. Paperback. Estado de conservación: New. Language: English . Brand New 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 textto initiate a student in this exciting branch of mathematics. -- Mathematical Gazette. Nº de ref. de la librería AAC9780486600451

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Descripción 1955. PAP. Estado de conservación: New. New Book.Shipped from US within 10 to 14 business days. Established seller since 2000. Nº de ref. de la librería IB-9780486600451

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Georg Cantor
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Descripción Dover Publications, 1955. Paperback. Estado de conservación: New. Never used!. Nº de ref. de la librería 0486600459

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Georg Cantor
Editorial: Dover Publications Inc., United States (1955)
ISBN 10: 0486600459 ISBN 13: 9780486600451
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Descripción Dover Publications Inc., United States, 1955. Paperback. Estado de conservación: New. Language: English . Brand New 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 textto initiate a student in this exciting branch of mathematics. -- Mathematical Gazette. Nº de ref. de la librería AAC9780486600451

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Descripción Dover Publications, 1955. Paperback. Estado de conservación: New. Brand New!. Nº de ref. de la librería 0486600459

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Descripción Dover Publications. PAPERBACK. Estado de conservación: New. 0486600459 BRAND NEW, GIFT QUALITY! NOT OVERSTOCKS OR MARKED UP REMAINDERS! DIRECT FROM THE PUBLISHER!|0.52. Nº de ref. de la librería OTF-S-9780486600451

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Descripción Dover Publications. PAPERBACK. Estado de conservación: New. 0486600459 *BRAND NEW* Ships Same Day or Next!. Nº de ref. de la librería NATARAJB1FI996710

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Descripción Paperback. Estado de conservación: New. Paperback. The famous articles, 1895-7, that founded a new branch of mathematics. Covers addition, multiplication and exponentiation of cardinal numbers, smallest transfinite cardinal numbers, ordina.Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 224 pages. 0.236. Nº de ref. de la librería 9780486600451

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