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Bundle_Gerbe comments on The Crackpot Offer - Less Wrong
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Eliezer, did you realize at the time that what you had done was construct the basic outline of the proof that 2^aleph0 = aleph1? There was an interesting gem hiding in your disproof, had you looked. Reversed stupidity is not intelligence, and all that :)
No 2^alpeh0=aleph1 is the continuum hypothesis, which is independent of the standard axioms of math, and can't be proven. I think maybe you mean he was close to showing 2^aleph0 is the cardinality of the reals, but I think he knew this already and was trying to use it as the basis of the proof.
Making mistakes like Eliezer's is a big part of learning math though, if we are looking for a silver lining. When you prove something you know is wrong, usually it's because of some misunderstanding or incomplete understanding, and not because of some trivial error. I think the diagonal argument seems like some stupid syntactical trick the first time you hear it, but the concept is far-reaching. Surely Eliezer came away with a bit better understanding of its implications after he straightened himself out.