Front cover image for Understanding the infinite

Understanding the infinite

How can the infinite, a subject remote from finite experience, be an everyday tool for working mathematicians? Blending history, philosophy, mathematics, and logic, Lavine answers this question with clarity. He demonstrates that knowledge of the infinite is possible, even according to strict standards requiring some intuitive basis for knowledge.
Print Book, English, 1998
2nd printing View all formats and editions
Harvard Univ. Press, Cambridge, Mass., 1998
IX, 372 Seiten : Diagramme ; 24 cm
9780674920965, 9780674921177, 0674920961, 0674921178
246402191
Introduction Infinity, Mathematics' Persistent Suitor Incommensurable Lengths, Irrational Numbers Newton and Leibniz Go Forward, and Faith Will Come to You Vibrating Strings Infinity Spurned Infinity Embraced Sets of Points Infinite Sizes Infinite Orders Integration Absolute vs. Transfinite Paradoxes What Are Sets? Russell Cantor Appendix: Letter from Cantor to Jourdain, 9 July 1904 Appendix: On an Elementary Question of Set Theory The Axiomatization of Set Theory The Axiom of Choice The Axiom of Replacement Definiteness and Skolem's Paradox Zermelo Go Forward, and Faith Will Come to You Knowing the Infinite What Do We Know? What Can We Know? Getting from Here to There Appendix Leaps of Faith Intuition Physics Modality Second-Order Logic From Here to Infinity Who Needs Self-Evidence? Picturing the Infinite The Finite Mathematics of Indefinitely Large Size The Theory of Zillions Extrapolations Natural Models Many Models One Model or Many? Sets and Classes Natural Axioms Second Thoughts Schematic and Generalizable Variables Bibliography Index