Real Numbers, Generalizations of the Reals, and Theories of Continua - Synthese Library Softcover reprint of hardcover 1st ed. 1994 edition

Marc Notes: All the contributors to this volume are outstanding authorities in their respective fields, and the essays, which are directed to 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. 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