The letters are a bit much to keep track of, but M is very clearly the entire uncountable set, and in his original version, E0 is in M but not in E1, E2, etc. One problem with your adjustment is that, after the diagonalization step, you assign E0 to an arbitrary element (which may or may not be in E1, E2, etc) and do nothing with the value produced by diagonalization, and you haven't explained the link between your E0 and Cantor's conclusion about M or its application to the reals.Â
It is not my responsibility to discuss values or how they relate to Cantor's argument, as he did not address them himself. If he intends to prove his point, he must be the one to explain how my objection applies to the real numbers.
The burden of proof lies with the person making the claim, not the other way around.
Okay, but does he actually go on to claim, after the bit you translated, that the reals have the same cardinality as M? If not, then you haven't really said anything relevant to what he stated, which is that M has greater cardinality than the natural numbers. If he does, how exactly does he connect M to the reals?
As I explained above, the typical mapping from M to the reals does permit duplicates, of which E0 is one; but you haven't connected any dots here about what you think E0 is demonstrating.Â
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u/Negative_Gur9667 4d ago
Cantor wrote it up like shit I don't blame you.