On 2 Apr., 02:06, Virgil <vir...@ligriv.com> wrote:
> > > Nevertheless Cantor has given a finite formula to construct the list > > of all rationals between 0 and 1. From that formula we can find every > > entry and the anti-diagonal up to every digit d_n. From that we can > > easily prove that for every FIS d_1, d_2, ..., d_n of d there are > > infinitely many rationals with the same FISs. For every finite number > > n - and there are no other lines than such enumerated with a finite > > number! > > But as there is no end to the set/list of natural/finite numbers, there > is also no end to the set/list of such lines.
What shall that "argument" be good for? Why should there be an end? If I say every natural number is divisible by 1 without remainder. Would you doubt that on the grounds that there is no end to the sequence of natural numbers? Such that possibly a natural number would follow that is not divisible by 1?