On 20 Feb., 23:27, William Hughes <wpihug...@gmail.com> wrote:
> > > > For every natural number n we have > > > the nth line of L and x > > > are not coFIS > > > > true?- > > > True > > Is the statement > > There is no natural number m > such that the mth line of L and x > are coFIS > > true?-
No, the statement is wrong. The true statement is: We cannot find the largest number such that the mth line and x are coFIS. Again you assume actual infinity for x.
Consider the union of ordered sets in ZF: (1, ) (1, 2, ) (1, 2, 3, )
Each set has a blank.
Or consider the union of natural numbers in a set B while there remains always one number in the intermediate reservoir A.
One would think that never all naturals can be collected in B, since a number n can leave A not before n+1 has arrived.
Of course this shows that ZF with its set of all natural numbers is contradicted. Presumably it is this recognition that raises your interest in potential infinity of analysis. There you can collect the natural numbers up to "every" n, although always infinitely many are missing.
Therefore the set 0 10 110 1110 ... has a line that is coFIS with 111... (up to every n - and more is not feasible).