On 22 Dez., 06:05, Zuhair <zaljo...@gmail.com> wrote: > On Dec 21, 8:44 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> Cantor's argument is about diagonalizing any > COUNTABLE set of reals. So again for any *countable* set S of reals > there is a diagonal r that differs from each real in S by a finite > initial segment n(r).
But each of these different initial segments n(r) is contained in another place of *that* Binary Tree which contains only all finite paths - hence is countable even in your opinion.
Therefore Cantor's argument here fails in case of an obviously countable set.
> This has been PROVED by Cantor
not considering the Binary Tree!
> This logically entails that the set R > of ALL reals cannot be countable,
and that it must be countable. ! > > A final word about your project. You tried to prove an "inconsistency" > with the assumption of uncountability of reals, which you couldn't > manage to carry out. And nobody managed and nobody could ever manage > because uncountability of reals is provable in very weak fragments of > Z actually of second order arithmetic, and those are PROVED to be > consistent.
From that you can see what a mess your "proofs" are. It's matheology. No serious person will give a dime for that nonsese.