Sets

ZFC and the infinite. Countability as the tipping point. A set containing every successor. Halmos on picking out the natural numbers from this requirement. Subsets of naturals giving the reals in a holy way. (Holy subsets...) Re-examine the notion that Feferman mentions: we don't have a grasp of "All functions from $N$ to $\{0,1\}$". So we don't appreciate the depth of such a reservoir. Binary trees (infinite: countable nodes, uncountable paths). Common errors in this sort of reasoning: Davies re monkeys. 2-dimensional binary tree as showing $[0,1]\times[0,1]$ similar to $[0,1]$.