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Understanding the infinite

Author: Shaughan Lavine
Publisher: Cambridge, Mass. : Harvard Univ. Press, 1998.
Edition/Format:   Print book : English : 2nd printingView all editions and formats
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How can the infinite, a subject remote from finite experience, be an everyday tool for working mathematicians? Blending history, philosophy, mathematics, and logic, Lavine answers this question with  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Shaughan Lavine
ISBN: 0674920961 9780674920965 0674921178 9780674921177
OCLC Number: 246402191
Description: IX, 372 Seiten : Diagramme ; 24 cm
Contents: Introduction Infinity, Mathematics' Persistent Suitor Incommensurable Lengths, Irrational Numbers Newton and Leibniz Go Forward, and Faith Will Come to You Vibrating Strings Infinity Spurned Infinity Embraced Sets of Points Infinite Sizes Infinite Orders Integration Absolute vs. Transfinite Paradoxes What Are Sets? Russell Cantor Appendix: Letter from Cantor to Jourdain, 9 July 1904 Appendix: On an Elementary Question of Set Theory The Axiomatization of Set Theory The Axiom of Choice The Axiom of Replacement Definiteness and Skolem's Paradox Zermelo Go Forward, and Faith Will Come to You Knowing the Infinite What Do We Know? What Can We Know? Getting from Here to There Appendix Leaps of Faith Intuition Physics Modality Second-Order Logic From Here to Infinity Who Needs Self-Evidence? Picturing the Infinite The Finite Mathematics of Indefinitely Large Size The Theory of Zillions Extrapolations Natural Models Many Models One Model or Many? Sets and Classes Natural Axioms Second Thoughts Schematic and Generalizable Variables Bibliography Index
Responsibility: Shaughan Lavine.

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Understanding the Infinite is a remarkable blend of mathematics, modern history, philosophy, and logic, laced with refreshing doses of common sense. It is a potted history of, and a philosophical Read more...

 
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