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100% Positive

Analyzed from 126 words in the discussion.

Trending Topics

#structure#countable#feel#small#contains#complexity#tree#larger#though#visualization

Discussion (8 Comments)Read Original on HackerNews

munchler•37 minutes 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•31 minutes 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•16 minutes ago
TREE(3) is unimaginably small, compared to ω
voidmain•28 minutes ago
The visualization is of the power set, which is uncountable.
michael0church•23 minutes 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•26 minutes ago
What a great visualization!

Now can your favorite LLM make me a similar one for the Real #s?

stavros•24 minutes ago
Why can't yours?
flobosg•about 1 hour ago
(2021)