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OverviewSince their appearance in the late 19th century, the Cantor-Dedekind theory of real numbers and philosophy of the continuum have emerged as pillars of standard mathematical philosophy. On the other hand, this period also witnessed the emergence of a variety of alternative theories of real numbers and corresponding theories of continua, as well as non-Archimedean geometry, non-standard analysis, and a number of important generalizations of the system of real numbers, some of which have been described as arithmetic continua of one type or another. With the exception of E.W. Hobson's essay, which is concerned with the ideas of Cantor and Dedekind and their reception at the turn of the century, the papers in the present collection are either concerned with, or are contributions to, the latter groups of studies. All the contributors are authorities in their respective fields, and the essays, which are directed at historians and philosophers of mathematics, as well as to mathematicians who are concerned with the foundations of their subject, are preceded by a lengthy historical introduction. Full Product DetailsAuthor: P. EhrlichPublisher: Springer Imprint: Springer Edition: 1994 ed. Volume: 242 Dimensions: Width: 15.60cm , Height: 1.90cm , Length: 23.40cm Weight: 1.390kg ISBN: 9780792326892ISBN 10: 079232689 Pages: 288 Publication Date: 30 September 1994 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Awaiting stock  The supplier is currently out of stock of this item. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out for you. Table of ContentsI. The Cantor-Dedekind Philosophy and Its Early Reception.- On the Infinite and the Infinitesimal in Mathematical Analysis (Presidential Address to the London Mathematical Society, November 13, 1902).- II. Alternative Theories of Real Numbers.- A Constructive Look at the Real Number Line.- The Surreals and Reals.- III. Extensions and Generalizations of the Ordered Field of Reals: The Late 19th-Century Geometrical Motivation.- Veronese’s Non-Archimedean Linear Continuum.- Review of Hilbert’s Foundations of Geometry (1902): Translated for the American Mathematical Society by E. V. Huntington (1903).- On Non-Archimedean Geometry. Invited Address to the 4th International Congress of Mathematicians, Rome, April 1908. Translated by Mathieu Marion (with editorial notes by Philip Ehrlich).- IV. Extensions and Generalizations of the Reals: Some 20th-Century Developments.- Calculation, Order and Continuity.- The Hyperreal Line.- All Numbers Great and Small.- Rational and Real Ordinal Numbers.- Index of Names.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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