??
There are an infinite number of diagonals in a list. For every coordinate, the are 4 diagonals, in an infinite list, there are an infinite number of coordinates.
Ok, name it what you want then *shrug* It's obviously pertinent that there are "closed lists" in real number list representation, particularly when the topic talks about diagonalization, which is what we're discussing. You blankly stated that Cantor proved once and for all, that diagonalization proved uncountability. That's not true, there are "closed lists". I just proved one right in front of you, why do I need a source for it to be proven to you?
Additionally, "closed lists" have been found for lists of irrationals, though the lists were shown to not be complete.
The open question is whether the incompleteness is inherent or whether it's a sequence problem?
Like I explained before, if you list all the counting numbers first, you can't list all the rationals "next", because the counting numbers go forever. BUT! You can interpolate them (called scattering) and if you scatter them, you can make a whole list of the rationals… to do this, the sequence has to be very precise. When adding irrationals, obviously, the only way to include them is to interpolate them with the rationals, because, again, the new list of all rationals goes on forever, and you can't tack the irrationals at "the end".
Cantor could have just run into a sequencing problem, and considered it a proof. We already know lists can be constructed that contain their diagonals - so the question isn't in my mind, resolved. You can argue dimensional flooding, and I can come back and say you have a sequencing problem… but to do this, I have to solve, not just state, the scattering sequence that proves the dimensional flooding can be listed - at least in order to prove you wrong.
In saying this, it is extremely easy to see dimensional flooding from a sequencing error, and assume it can't be done, when all it really is, is a sequencing error.