Understanding the infinite
Choice Reviews Online · 1995
Part 1 Introduction. Part 2 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. Part 3 Sets of points: infinite sizes infinite orders integration absolute versus transfinite paradoxes. Part 4 What are sets?: Russell Cantor appendix A - letter from Cantor to Jourdain, 9 July 1904 appendix B - on an elementary question of set theory. Part 5 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. Part 6 Knowing the infinite: what do we know? what can we know? getting from here to there. Part 7 Leaps of faith: intuition physics modality second-order logic. Part 8 From here to infinity: who needs self-evidence? picturing the infinite the finite mathematics of indefinitely large size the theory of zillions. Part 9 Extrapolations: natural models many models one model or many? sets and classes natural axioms second thoughts schematic and generalizable variables.