Understanding the InfiniteHow can the infinite, a subject so remote from our finite experience, be an everyday working tool for the working mathematician? Blending history, philosophy, mathematics and logic, Shaughan Lavine answers this question with clarity. An account of the origins of the modern mathematical theory of the infinite, his book is also a defense against the attacks and misconceptions that have dogged this theory since its introduction in the late 19th century. |
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Lietotāja recenzija - fpagan - LibraryThingDeep discussion of the mathematical work of Cantor et al, and proposal for "a finite mathematics of indefinitely large size." Lasīt pilnu pārskatu
Saturs
Introduction | 1 |
II Infinity Mathematics Persistent Suitor | 11 |
1 Incommensurable Lengths Irrational Numbers | 12 |
2 Newton and Leibniz | 15 |
3 Go Forward and Faith Will Come to You | 22 |
4 Vibrating Strings | 26 |
5 Infinity Spurned | 32 |
6 Infinity Embraced | 37 |
Knowing the Infinite 1 What Do We Know? | 154 |
2 What Can We Know? | 162 |
3 Getting from Here to There | 181 |
4 Appendix | 203 |
Leaps of Faith 1 Intuition | 213 |
2 Physics | 218 |
3 Modality | 221 |
4 SecondOrder Logic | 224 |
Sets of Points 1 Infinite Sizes | 42 |
2 Infinite Orders | 44 |
3 Integration | 49 |
5 Paradoxes | 57 |
What Are Sets? 1 Russell | 63 |
2 Cantor | 76 |
Letter from Cantor to Jourdain 9 July 1904 | 98 |
On an Elementary Question of Set Theory | 99 |
1 The Axiom of Choice | 103 |
2 The Axiom of Replacement | 119 |
3 Definiteness and Skolems Paradox | 123 |
4 Zermelo | 134 |
5 Go Forward and Faith Will Come to You | 141 |
1 Who Needs SelfEvidence? | 241 |
2 Picturing the Infinite | 246 |
3 The Finite Mathematics of Indefinitely Large Size | 267 |
4 The Theory of Zillions | 288 |
Extrapolations 1 Natural Models | 309 |
2 Many Models | 314 |
3 One Model or Many? Sets and Classes | 316 |
4 Natural Axioms | 320 |
5 Second Thoughts | 322 |
6 Schematic and Generalizable Variables | 325 |
Bibliography | 329 |
| 349 | |
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accept actually allow analysis apply argument arithmetic assumption axiomatic axioms basis bound called Cantor cardinal Choice claim clear collections combinatorial commitment conception concerning consider consistent construction counted defined definition detail developed discussed domain elements example existence experience expressions extrapolation fact finitary finite mathematics finite set first-order follows formal Foundation function give given idea important indefinitely large infinite interpretation introduced intuition involved iterative knowledge least less limit logic mathematicians means natural numbers noted notion objects obtained ordinal numbers paradoxes physics position possible present principle problem proof prove quantifiers range rational real numbers reason relation Replacement restriction result rule Russell schematic second-order second-order logic seems self-evident sense sentence sequence set theory suggested symbols theorem things tion true truth understanding universe usual values variables well-ordered Zermelo
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Bibliogrāfiskā informācija
| Nosaukums | Understanding the Infinite |
| Autors | Shaughan LAVINE |
| Izdevums: | ilustrēts |
| Izdevējs | Harvard University Press, 1994 |
| ISBN | 0674920961, 9780674920965 |
| Apjoms | 372 lappuses |
| Eksportēt avotu | BiBTeX EndNote RefMan |