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munchler 1 hours ago [-]
What a beautiful illustration. It makes intuitive the very abstract concepts discussed in the text. It’s fun to zoom in and browse around the structure.
michael0church 1 hours ago [-]
It’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.
zaebal 1 hours ago [-]
TREE(3) is unimaginably small, compared to ω
zygentoma 8 minutes ago [-]
Well, any natural number is unimaginably small, compared to ω …
voidmain 1 hours ago [-]
The visualization is of the power set, which is uncountable.
michael0church 1 hours ago [-]
Right. But because it’s the smallest structure of its type (speaking loosely) it feels like something we should have a grasp on, even though it contains more complexity than we could ever describe or compute with (since both of those are countable.)
gregw2 1 hours ago [-]
What a great visualization!
Now can your favorite LLM make me a similar one for the Real #s?
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.
Now can your favorite LLM make me a similar one for the Real #s?