Real Numbers, Generalizations of the Reals, and Theories of Continua

Since 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 a...

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Corporate Author: SpringerLink (Online service)
Other Authors: Ehrlich, P. (Editor)
Format: eBook
Published: Dordrecht Springer Netherlands 1994, 1994
Edition:1st ed. 1994
Series:Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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