Real Numbers, Generalizations of the Reals, and Theories of Continua - Synthese Library 1994 edition

Marc Notes: Includes bibliographical references and index. Table of Contents: Part 0: General Introduction; P. Ehrlich. Part I: The Cantor--Dedekind Philosophy and its Early Reception. On the Infinite and Infinitesimal in Mathematical Analysis, Presidential Address to the London Mathematical Society, November 13, 1902, E. W. Hobson. Part II: Alternative Theories of Real Numbers. A Constructive Look at the Real Number Line; D. S. Bridges. The Surreals and Reals; J. H. Conway. Part III: Extensions and Generalizations of the Ordered Field of Reals: the Late 19th-Century Geometrical Motivation. Veronese's Non-Archimedean Linear Continuum; G. Fisher. Review of Hilbert's Foundations of Geometry; Henri Poincare (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, Giuseppe Veronese; Translated by Mathieu Marion (with editorial notes by Philip Ehrlich). Part IV: Extensions and Generalizations of the Reals: Some 20th-Century Developments. Calculation, Order, and Continuity; H. Sinaceur. The Hyperreal Line; H. J. Keisler. All Numbers Great and Small; P. Ehrlich. Rational and Real Ordinal Numbers; D. Klaua."

Contributor Bio:  Ehrlich, P fm.author_biographical_note1