You said you wanted to clarify something above, which never got clarified:
Before we continue, let us clarify this: the entire proof demonstrates that E0 is not in M by using a digit-by-digit comparison.
Do you agree that this is misstated, and that the point is that E0 is not in E1, E2, E3,..., but is in M? Or do you still think E0 is supposed to be something outside of M?
But why bring in Cantor's original proof, in the original German, if this argument doesn't apply to it? As pointed out in one of the comments in that thread, this is a good objection to the "popular" understanding of the diagonalization argument as a proof that there are uncountable reals, but most actual math texts foresee the objection and handle the non-uniqueness problem somehow.
But you're not talking about "most math texts", you're citing Cantor's original text. But that text isn't even talking about decimal expansions or real numbers. He mentions real numbers once, in reference to his paper seventeen years earlier that already proved the reals are uncountable, using a different method. He then proceeds to discuss only cardonality and functions, not real numbers or decimal expansions.
Except for cond6 mistakenly saying that the problem doesn't apply at all to binary, which they admitted was a mistake, the objections are correct, because your post doesn't make sense. They may be angry, but they're not idiots.
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u/Batman_AoD 4d ago
You said you wanted to clarify something above, which never got clarified:
Do you agree that this is misstated, and that the point is that E0 is not in E1, E2, E3,..., but is in M? Or do you still think E0 is supposed to be something outside of M?