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.
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.