Understanding the infinite
著者
書誌事項
Understanding the infinite
Harvard University Press, 1998
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注記
"First Harvard University Press paperback edition" -- T.p. verso
Originally published: 1994
内容説明・目次
内容説明
How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that require some intuitive basis for knowledge.
目次
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
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