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.
"synopsis" may belong to another edition of this title.
"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."
"About this title" may belong to another edition of this title.
FREE shipping within United Kingdom
Destination, rates & speedsSeller: Goldstone Books, Llandybie, United Kingdom
paperback. Condition: Good. All orders are dispatched within one working day from our UK warehouse. We've been selling books online since 2004! We have over 750,000 books in stock. No quibble refund if not completely satisfied. Seller Inventory # mon0007501157
Quantity: 1 available
Seller: ThriftBooks-Dallas, Dallas, TX, U.S.A.
Paperback. Condition: Fair. No Jacket. Readable copy. Pages may have considerable notes/highlighting. ~ ThriftBooks: Read More, Spend Less 0.57. Seller Inventory # G0486600459I5N00
Quantity: 1 available
Seller: Better World Books, Mishawaka, IN, U.S.A.
Condition: Good. Used book that is in clean, average condition without any missing pages. Seller Inventory # 594994-6
Quantity: 1 available
Seller: Better World Books, Mishawaka, IN, U.S.A.
Condition: Good. Former library book; may include library markings. Used book that is in clean, average condition without any missing pages. Seller Inventory # GRP36887684
Quantity: 2 available
Seller: WorldofBooks, Goring-By-Sea, WS, United Kingdom
Paperback. Condition: Very Good. The book has been read, but is in excellent condition. Pages are intact and not marred by notes or highlighting. The spine remains undamaged. Seller Inventory # GOR005301103
Quantity: 1 available
Seller: Plurabelle Books Ltd, Cambridge, United Kingdom
Paperback. Condition: Very Good. 211p paperback with pictorial cover and decorative border, pages clean and unmarked, very good Language: English. Seller Inventory # 66127
Quantity: 1 available
Seller: Revaluation Books, Exeter, United Kingdom
Paperback. Condition: Brand New. 224 pages. 8.00x5.50x0.50 inches. In Stock. Seller Inventory # __0486600459
Quantity: 1 available
Seller: Gulf Coast Books, Cypress, TX, U.S.A.
paperback. Condition: Good. Seller Inventory # 0486600459-3-34549361
Quantity: 1 available
Seller: Emily Green Books, North Shields, United Kingdom
Soft cover. Condition: Very Good. 1st Edition. 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
Quantity: 1 available
Seller: West Coast Bookseller, Moorpark, CA, U.S.A.
paperback. Condition: As New. Seller Inventory # M3-6-25BB
Quantity: 1 available