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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| Format: | eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
1994, 1994
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| Edition: | 1st ed. 1994 |
| Series: | Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science
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| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- I. 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