The more I hear about Cantor's diagonal argument the more holes there seem to be in it. I have never seen anyone genuinely work to defend it against a determined skeptic.It seems like all infinities would indeed be the same size to me. I'm interested in seeing if anyone here would care to present, and then defend against questioning, the diagonal argument.
It's related to the fact that no set can surject onto its own power set. No assumptions about the cardinality of X are necessary, so this is enough to show that more than one infinite cardinal exists.This strategy of using a "flipped diagonal" to get a contradiction goes beyond Cantor. It comes up in the proofs of Gödel's theorems and the unsolvability of the halting problem among other things. All of these are ultimately variations of the liar paradox.
>>18486920we really should have a list of trolling topics like this one, or 0.999... = 1 etc., with an automatic ban attached.
>>18486920He was Jewish and the concept of infinity is fraudulent
>>18487012Thanks anon, seeing it laid out like this it makes total sense after you think about it for a bit, I would now consider myself persuaded
>>18487673Are you OP? If so, that was quick, were you not determined enough or not skeptical enough and what "holes" were you talking about if you didn't even have a counterpoint to a fairly brief fpbp?
>>18488057I am OP. I had just been hearing it from people who didn't know what they were talking about and/or were presenting it in extremely poor ways. Once someone lays out the logic itself there's not much to argue with really.
>>18488286But what were the "holes" you originally mentioned since you implied that the logic had been laid out for you and you found numerous holes in it.
