On Friday, 14 June 2013 10:16:05 UTC+2, Zeit Geist wrote:
> > 1) The Binary Tree containing all rational numbers of the unit interval does not contain any irrational number.
> You are incorrect.
> > 2) The triangle construcuted in 3-symmetry is and always remains equilateral.
> Yes, but the stament above is wrong.
No, it is the same fact. Let the triangle remain equilateral. A line does not contain aleph_0 1's. Hence the first column and diagonal do not contain aleph_0 1's either. A path in the Binary Tree does not contain aleph_0 nodes. The Binary Tree does not contain paths of irrational numbers.