Real Numbers, Generalizations of the Reals, and Theories of ContinuaP. Ehrlich Springer Science & Business Media, 29 de juny 2013 - 288 pàgines 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 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 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. |
Continguts
E W HOBSON On the Infinite and the Infinitesimal | 3 |
DOUGLAS S BRIDGES A Constructive Look at the Real | 28 |
J H CONWAY The Surreals and Reals | 93 |
EXTENSIONS AND GENERALIZATIONS OF | 104 |
HENRI POINCARÉ Review of Hilberts Foundations | 147 |
GIUSEPPE VERONESE On NonArchimedean Geometry | 169 |
HOURYA SINACEUR Calculation Order and Continuity | 191 |
H JEROME KEISLER The Hyperreal Line | 207 |
PHILIP EHRLICH All Numbers Great and Small 239 | 238 |
DIETER KLAUA Rational and Real Ordinal Numbers | 259 |
277 | |
Altres edicions - Mostra-ho tot
Real Numbers, Generalizations of the Reals, and Theories of Continua P. Ehrlich Previsualització no disponible - 2010 |
Real Numbers, Generalizations of the Reals, and Theories of Continua P. Ehrlich Previsualització no disponible - 2012 |
Frases i termes més freqüents
a₁ abstract aggregate algebraic analysis Archimedean axiom arithmetic Artin axiom of Archimedes binary sequence Cantor Cauchy sequence classical concept continuous continuum convergence countable Dedekind defined definition dist(x elements equal equivalent example exists finite number function given Hahn hyperfinite hyperfinite grid hyperreal line hyperreal number system hypothesis infinitely large infinitesimal integer interval intuition ISBN Keisler Levi-Civita located Loeb measure logical magnitude Math mathematicians multiplication natural numbers non-Archimedean non-Archimedean geometry non-Archimedean system non-Euclidean geometry Nonstandard Analysis nonvoid notion objects ordered field ordered group ordinal numbers paraconvex Philosophy positive integer postulate Professor Hilbert proof properties prove rational numbers real closed real closed fields real line real numbers real-closed ordered field rectilinear recursive relation Science Section segment set theory space Stolz straight line subset surreal theorem totally bounded transfinite translation ultrapower Veronese Veronese's x₁