On Friday, 20 December 2013 15:56:54 UTC+1, wpih...@gmail.com wrote: > To be precise: > > > > There is no potentially infinite list of potentially infinite 0/1 > > sequences, L, with the property that any potentially infinite 0/1 sequence > > is in L
Correct. In my example with the rationals-complete list I assume actual infinity. But even in this branch of matheology there is no antidiagonal with more digits than all d_n, n in |N.
And if d never differs from all rationals, then there are rationals which parallel d up to every digit. Numbers which are parallel (identical) up to every digit are identical numbers.
In fact, however, numbers are not given by digits but by a finite formula. That means d, defined by a finite formula, differs in fact from all rational numbers of the list. But that cannot be shwon by digits.