The Continuity Debate: Dedekind, Cantor, du Bois-Reymond, and Peirce on Continuity and Infinitesimals - Couverture souple

Buckley, Benjamin Lee

 
9780983700487: The Continuity Debate: Dedekind, Cantor, du Bois-Reymond, and Peirce on Continuity and Infinitesimals
Couverture souple
ISBN 10 : 0983700486 ISBN 13 : 9780983700487
Editeur : Docent Press, 2012

Synopsis

The topic of this book is the historical struggle to define and defend a real number continuum which could do the work limit theory required of it. These definitions drew heavily on philosophical and foundational assumptions, and each raises numerous philosophical questions of its own. As we shall see, attempts to formulate a non-geometrical mathematical continuity raise questions such as: What is a number? What, in particular, is a real number? What is the true nature of continuity itself? Does a philosophically coherent definition of continuity logically commit us to infinitesimally small quantities? Is the concept of an infinitesimally small quantity even logically coherent? What is the relationship between this real number continuum and other well known continua, such as the geometrical straight line? The main question to be addressed, of course, is whether mathematical continuity exists at all.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

The topic of this book is the historical struggle to define and defend a real number continuum which could do the work limit theory required of it. These definitions drew heavily on philosophical and foundational assumptions, and each raises numerous philosophical questions of its own. As we shall see, attempts to formulate a non-geometrical mathematical continuity raise questions such as: What is a number? What, in particular, is a real number? What is the true nature of continuity itself? Does a philosophically coherent definition of continuity logically commit us to infinitesimally small quantities? Is the concept of an infinitesimally small quantity even logically coherent? What is the relationship between this real number continuum and other well known continua, such as the geometrical straight line? The main question to be addressed, of course, is whether mathematical continuity exists at all.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Docent Press
Date d'édition
2012
Langue
anglais
ISBN 10 
0983700486
ISBN 13 
9780983700487
Reliure
Broché
Nombre de pages
182
Coordonnées du fabricant
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