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Book Description Condition: New. Seller Inventory # 28963627-n
Book Description Hardcover. Condition: new. Seller Inventory # 9780198712749
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Book Description Hardcover. Condition: new. Hardcover. 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 AbrahamRobinson), 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, includingEuclidean and non-Euclidean geometries, that are mathematically equivalent (inter-reducible) to the currently standard, point-based accounts in mainstream mathematics. Hellman and Shapiro explore the development of the idea of the continuous, from the Aristotelian view that a true continuum cannot be composed of points to the now standard, entirely punctiform frameworks for analysis and geometry. They then investigate the underlying metaphysical issues concerning the nature of space or space-time. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780198712749
Book Description Condition: New. Seller Inventory # 28963627-n
Book Description Hardcover. Condition: Brand New. 208 pages. 9.25x6.50x1.00 inches. In Stock. Seller Inventory # x-019871274X
Book Description Hardback. Condition: New. This item is printed on demand. New copy - Usually dispatched within 5-9 working days. Seller Inventory # C9780198712749
Book Description Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Hellman and Shapiro explore the development of the idea of the continuous, from the Aristotelian view that a true continuum cannot be composed of points to the now standard, entirely punctiform frameworks for analysis and geometry. They then investigate th. Seller Inventory # 219925146