Téléchargez le livre : Varieties of Continua

Varieties of Continua

From Regions to Points and Back de

,

Éditeur :

OUP Oxford


Paru le : 2018-02-02

eBook Téléchargement , DRM LCP 🛈 DRM Adobe 🛈
Lecture en ligne (streaming)
43,11 €
Téléchargement immédiat
Dès validation de votre commande
Image Louise Reader présentation

Louise Reader

Lisez ce titre sur l'application Louise Reader.

badge apple Application Louise Reader
badge Android Application Louise Reader
Description
Varieties of Continua explores the development of the idea of the continuous. Hellman and Shapiro begin with two historical episodes. The first is the remarkably rapid transition in the course of the nineteenth century from the ancient Aristotelian view, that a true continuum cannot be composed of points, to the now standard, point-based frameworks for analysis and geometry found in modern mainstream mathematics (stemming from the work of Bolzano, Cauchy, Weierstrass, Dedekind, Cantor, et al.). The second is the mid-tolate-twentieth century revival of pre-limit methods in analysis and geometry using infinitesimals including non-standard analysis (due to Abraham Robinson), and the more radical smooth infinitesimal analysis that uses intuitionistic logic. Hellman and Shapiro present a systematic comparison of these and related alternatives (including constructivist and predicative conceptions), weighing various trade-offs, helping articulate a modern pluralist perspective, and articulate a modern pluralist perspective on continuity. The main creative work of the book is the development of rigorous regions-based theories of classical continua, including Euclidean and non-Euclidean geometries, that are mathematically equivalent (inter-reducible) to the currently standard, point-based accounts in mainstream mathematics.
Pages
224 pages
Collection
n.c
Parution
2018-02-02
Marque
OUP Oxford
EAN papier
9780191021350
EAN PDF
9780191021350
Informations sur l'ebook
Nombre pages copiables
0
Nombre pages imprimables
0
Taille du fichier
4004 Ko
Prix
43,11 €

Suggestions personnalisées