Understanding the InfiniteHarvard University Press, 1998. gada 13. janv. - 376 lappuses 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. |
Saturs
I Introduction | 1 |
II Infinity Mathematics Persistent Suitor | 11 |
III Sets of Points | 42 |
IV What Are Sets? | 63 |
V The Axiomatization of Set Theory | 103 |
VI Knowing the Infinite | 154 |
VII Leaps of Faith | 213 |
VIII From Here to Infinity | 241 |
IX Extrapolations | 309 |
Bibliography | 329 |
| 349 | |
Citi izdevumi - Skatīt visu
Bieži izmantoti vārdi un frāzes
actually analysis argument Axiom of Choice Axiom of Replacement axiomatic set theory background set theory Cantor Cantorian cardinal combinatorial collections commitment consistent construction Continuum Hypothesis counted defined definition denumerable discussed epistemic example extrapolation fact Fin(PA Fin(T Fin(ZFC finitary finitary mathematics finite mathematics finite set theory finitist first-order logic formal Foundation Fourier Fraenkel Frege function ƒ given Gödel hfpsets Hilbert idea indefinitely large infinitary infinite sets infinity intuition intuitionist irrational numbers isomorphic iterative conception Leibniz limit mathematical objects mathematicians N₁ natural model natural numbers Neumann normal domain notion ordinal numbers paradoxes Peano arithmetic philosophy of mathematics possible Power Set predecessors primitive recursive principle problem proof propositional functions prove quantifiers rational numbers real numbers relation Replacement result Russell Russell's schematic variables second-order logic second-order set theory self-evident sense sentence sequence set-theoretic Skolem subset symbols theorem tion transfinite true truth well-ordered set Zermelo