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Understanding the infinite /
How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Shaughan Levine attempts to answer this question using a blend of history, philosophy, mathematics and logic.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, Mass. :
Harvard University Press,
1998.
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| Edición: | 1st Harvard University Press pbk. ed. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Lavine, Shaughan. | |
| 245 | 1 | 0 | |a Understanding the infinite / |c Shaughan Lavine. |
| 250 | |a 1st Harvard University Press pbk. ed. | ||
| 260 | |a Cambridge, Mass. : |b Harvard University Press, |c 1998. | ||
| 300 | |a 1 online resource (ix, 372 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 500 | |a Originally published 1994. | ||
| 504 | |a Includes bibliographical references (pages 329-347) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 4. Appendix B: On an Elementary Question of Set TheoryV. 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 | |
| 505 | 8 | |a 3. The Finite Mathematics of Indefinitely Large Size4. 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 | |
| 520 | |a How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Shaughan Levine attempts to answer this question using a blend of history, philosophy, mathematics and logic. | ||
| 520 | |b How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working of a mathematician? Blending history, philosophy, mathematics, and logic, the author seeks to answers this question. 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. | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
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| 650 | 0 | |a Mathematics |x Philosophy. | |
| 650 | 6 | |a Mathématiques |x Philosophie. | |
| 650 | 7 | |a MATHEMATICS |x Set Theory. |2 bisacsh | |
| 650 | 7 | |a PHILOSOPHY |x General. |2 bisacsh | |
| 650 | 7 | |a Mathematics |x Philosophy. |2 fast |0 (OCoLC)fst01012213 | |
| 653 | 0 | |a Sets (Mathematics) | |
| 776 | 0 | 8 | |i Print version: |a Lavine, Shaughan. |t Understanding the infinite. |b 1st Harvard University Press pbk. ed. |d Cambridge, Mass. : Harvard University Press, 1998 |z 0674921178 |z 9780674921177 |w (DLC) 93049697 |w (OCoLC)42201841 |
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