Understanding the Infinite
Harvard University Press, 30 jun. 2009 - 384 páginas
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.
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Deep discussion of the mathematical work of Cantor et al, and proposal for "a finite mathematics of indefinitely large size." Leer reseña completa
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accept actually analysis arbitrary argument Axiom of Choice Axiom of Replacement axiomatic 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(T Fin(ZFC finitary finitary mathematics finite mathematics finite set theory first-order logic formal Foundation Fourier Fraenkel Frege given Godel hfpsets Hilbert idea indefinitely large infinitary infinite sets infinity intuition intuitionist irrational numbers isomorphic iterative conception Leibniz limit mathematical objects mathematicians 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 quasi-categoricity rational numbers real numbers reason 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