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Springer Real Numbers and Theories of Continua - Springer Philosophy

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Description

Explore the foundations of mathematical philosophy with this comprehensive examination of real numbers and continua theories. Since the late 19th century, the Cantor-Dedekind theory has dominated standard mathematical thought, yet alternative approaches have flourished alongside it. This volume investigates non-Archimedean geometry, non-standard analysis, and various generalisations of the real number system, including arithmetic continua of multiple types. Drawing on historical perspectives and philosophical frameworks, the work traces how these competing theories have shaped modern mathematics and challenged conventional understandings of mathematical structure. Essential reading for philosophers of mathematics, mathematicians interested in foundational issues, and scholars exploring the intellectual history of mathematical thought and its philosophical implications.

Key Features

Examines the Cantor-Dedekind theory of real numbers and its philosophical significance in modern mathematics.

Covers non-Archimedean geometry and non-standard analysis as alternatives to classical real number systems.

Investigates various generalizations of real numbers and their corresponding continua theories.

Part of the Synthese Library series, volume 242, providing scholarly depth for academic audiences.

Addresses the philosophical foundations underlying different mathematical approaches to continuity and real numbers.

Product Specifications

Format
paperback
Domain
Amazon UK
Release Date
07 December 2010
Listed Since
20 September 2010

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