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Chris Liss14d ago
No, it's the proof that the set of reals is larger than the set of natural numbers, even though the set of odds numbers is exactly the same size as the set of naturals. The proof is that you could match odds and naturals 1 to 1 forever. Match 1 with 1, 2 with 3, 3 with 5, 4 with 7, etc. You're not gonna run out of odds. But if you try to match naturals with reals, you run out. 1 with 1.01. 2 with 1.001, 3 with 1.0001. Etc. You will run out of naturals before you get anywhere.
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SuiGenerisJohn14d ago
Holy shit there is a proof of that? That, is not intuitive. Particularly when you compare it to the non-galaxy brain intuition you can derive from the infinite hotel thought experiment.
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