Am Montag, 9. Dezember 2013 20:13:31 UTC+1 schrieb wpih...@gmail.com:
> Note that this is sufficient to show there is no constructable list L,
Cantor's enumeration of the rationals is a construction.
> for > > which for any constructable 0/1 list y, y is in L. (Proof is by contradiction, > > assume L exists, then from y is in L we conclude that we can find an > > n in N such that y is the nth element of L. Contradiction. Thus L does not > > exist)
I am not interested in your "proofs" but in defining an irrational number like the antidiagonal d by an arbitrarily large sequence of its digits d_n (including an infinite sequence). This is impossible because for every digits d_n there are infinitely many duplicates.
If your proof supplies a contradiction, then set theory is self contradictory. q.e.d.