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 \([0,1]\).
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