If that’s truly your remaining objection, then I think that you should retract the unmerited criticisms about how they’re trying to prove 0.9999… != 1 or whatever. In my opinion, you have confidently misrepresented their arguments, and the discussion would benefit from your revisions.
This point seems right to me: if the post is specifically about representable functions than that is a valid formalization AFAICT. (Though a extremely cursed formalization for reasons mentioned in a variety of places. And if you dropped “representable”, then it’s extremely, extremely cursed for various analysis related reasons, though I think there is still a theoretically sound uniform measure maybe???)
It would also be nice if the original post:
Clarified that the rebuttal is specifically about a version of the counting-argument which counts functions.
Noted that people making counting arguments weren’t intending to count functions, though this might be a common misconception about counting arguments. (Seems fine to also clarify that existing counting arguments are too hand wavy to really engage with if that’s the view also.) (See also here.)
This point seems right to me: if the post is specifically about representable functions than that is a valid formalization AFAICT. (Though a extremely cursed formalization for reasons mentioned in a variety of places. And if you dropped “representable”, then it’s extremely, extremely cursed for various analysis related reasons, though I think there is still a theoretically sound uniform measure maybe???)
It would also be nice if the original post:
Clarified that the rebuttal is specifically about a version of the counting-argument which counts functions.
Noted that people making counting arguments weren’t intending to count functions, though this might be a common misconception about counting arguments. (Seems fine to also clarify that existing counting arguments are too hand wavy to really engage with if that’s the view also.) (See also here.)