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Understanding the infinite

Author: Shaughan Lavine
Publisher: Cambridge, Mass. : Harvard University Press, 1998.
Edition/Format:   eBook : Document : English : 1st Harvard University Press pbk. edView all editions and formats
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Lavine, Shaughan.
Understanding the infinite.
Cambridge, Mass. : Harvard University Press, 1998
(DLC) 93049697
(OCoLC)42201841
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Shaughan Lavine
ISBN: 9780674039995 0674039998
OCLC Number: 432695222
Notes: Originally published 1994.
Description: 1 online resource (ix, 372 pages) : illustrations
Contents: ""Preface""; ""Contents""; ""I. Introduction""; ""II. Infinity, Mathematics� Persistent Suitor""; ""1. Incommensurable Lengths, Irrational Numbers""; ""2. Newton and Leibniz""; ""3. Go Forward, and Faith Will Come to You""; ""4. Vibrating Strings""; ""5. Infinity Spurned""; ""6. Infinity Embraced""; ""III. Sets of Points""; ""1. Infinite Sizes""; ""2. Infinite Orders""; ""3. Integration""; ""4. Absolute vs. Transfinite""; ""5. Paradoxes""; ""IV. What Are Sets?""; ""1. Russell""; ""2. Cantor""; ""3. Appendix A: Letter from Cantor to Jourdain, 9 July 1904"" ""4. Appendix B: On an Elementary Question of Set Theory""""V. The Axiomatization of Set Theory""; ""1. The Axiom of Choice""; ""2. The Axiom of Replacement""; ""3. Definiteness and Skolem�s Paradox""; ""4. Zermelo""; ""5. Go Forward, and Faith Will Come to You""; ""VI. Knowing the Infinite""; ""1. What Do We Know?""; ""2. What Can We Know?""; ""3. Getting from Here to There""; ""4. Appendix""; ""VII. Leaps of Faith""; ""1. Intuition""; ""2. Physics""; ""3. Modality""; ""4. Second-Order Logic""; ""VIII. From Here to Infinity""; ""1. Who Needs Self-Evidence?""; ""2. Picturing the Infinite"" ""3. The Finite Mathematics of Indefinitely Large Size""""4. The Theory of Zillions""; ""IX. Extrapolations""; ""1. Natural Models""; ""2. Many Models""; ""3. One Model or Many? Sets and Classes""; ""4. Natural Axioms""; ""5. Second Thoughts""; ""6. Schematic and Generalizable Variables""; ""Bibliography""; ""Index""
Responsibility: Shaughan Lavine.

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