alt Hacker NewsIt’s also genuinely surprising. We’re used to thinking of the countable as the small infinity, which it is, and yet a structure we feel like we can visualize contains so much complexity.
There is also, weirdly, a way in which massive finite numbers like TREE(3) “feel” larger than N, and large countable infinities “feel” larger than w_1, even though the opposite is clearly true.
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aeneasmackenzie • today at 3:17 PM
All describable or recognizable complexity is part of the subcountable set of computable subsets of N. Higher infinities thus mostly contain fake elements about which nothing can be said, so they don’t feel any bigger.
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The visualization is of the power set, which is uncountable.