PHILOS 146 Lecture Notes - Lecture 20: Veblen Function, Limit Point, Set Theory
Document Summary
Cantor 1845-1918 important way of representing functions: 1/2ao + sum(an sinnx + bncosnx) a, topology, point set, set theory c. Limit: weakness thinks he can introduce a symbol. In the interval 0,1 every point is a limit point c. ii. P" = the set of limit point of p: the set of natural numbers can be put in one-one correspondence with set of integers, as with the rationals, but what about the reals? b. i. b. ii. b. iii. Assume there is a 1=1 onto mapping between |n and [0,1] There are many more real numbers than there are natural numbers b. iii. 1. the number of nonalgebraic number among the reals is much larger than the algebraic ones b. iii. 2. Does not prove a way to construct transcendental numbers: two sets have the same power iff there is a one-one onto mapping between them, problem of the continuum.
