{"product_id":"contributions-to-the-founding-of-the-theory-of-transfinite-numbers-dover-books-on-mathematics","title":"Contributions to the Founding of the Theory of Transfinite Numbers (Dover Books on Mathematics)","description":"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.\nCantor 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.\nAn 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.\n\"Would serve as well as any modern textto initiate a student in this exciting branch of mathematics.\" — Mathematical Gazette.\u003cbr\u003eASIN: 0486600459\u003cbr\u003eVSKU: DBV.0486600459.G\u003cbr\u003eCondition: Good\u003cbr\u003eAuthor\/Artist:Georg Cantor\u003cbr\u003eBinding: Paperback\u003cbr\u003e\u003cb\u003eNote:\u003c\/b\u003e Any images shown are stock photographs and product may differ from what is shown.  \u003cbr\u003e\u003cb\u003eCondition Notes\u003c\/b\u003e: Gently used with minimal wear on the corners and cover. A few pages may contain light highlighting or writing, but the text remains fully legible. Dust jacket may be missing, and supplemental materials like CDs or codes may not be included. May be ex-library with library markings. Ships promptly!  \u003cbr\u003e","brand":"Dream Books Co.","offers":[{"title":"Default Title","offer_id":41705732014138,"sku":"DBV.0486600459.G","price":7.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0555\/6011\/0138\/files\/0486600459-0.jpg?v=1790571119","url":"https:\/\/shop.dreambooksco.com\/products\/contributions-to-the-founding-of-the-theory-of-transfinite-numbers-dover-books-on-mathematics","provider":"Dream Books Co.","version":"1.0","type":"link"}