Understanding the Infinite

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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

Índice

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
Index
349
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Sobre el autor (2009)

Shaughan Lavine is Associate Professor of Philosophy at the University of Arizona.

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