On Friday, June 14, 2013 11:48:27 AM UTC-7, muec...@rz.fh-augsburg.de wrote: > On Friday, 14 June 2013 20:39:08 UTC+2, Virgil wrote: > > > In article <email@example.com>, firstname.lastname@example.org wrote: > On Friday, 14 June 2013 10:11:40 UTC+2, Julio Di Egidio wrote: > > >>The Binary Tree > > > Please show what relationship you have in mind, between the complete binary > > tree and the rationals "written in the usual manner", as I cannot guess > > what you have in mind. > > In the usual way, you write the numbers separately. Example: In the list > 0.1 > 0.11 > 0.111 > ... > you can look at every line, you will not find 1/9. You can also look at every line of that list above and not find most of the binary rationals that should properly appear even in WM's supposed trees. > > > > The list above contains only one path of the tree, that one at the outmost right side. > > > > 2) The triangle construcuted in 3-symmetry is equilateral. How does WM manage to have equilateral triangles each with one right angle and a couple of half-right angles in the finite case, and only one right angle and no other angles in the infinite case?? > > > > Not at all. There is no infinite case. > > > > > > a > > > > > > a > > bb > > > > > > c > > ac > > bbc > > > > > > infinite means, it goes on and on without end or limit or limit case. > How naive you are. Are still living in Ancient Greece.
Definition: A set, X, is infinite iff there exists a function, F and a subset Y of X, such that F: X --> Y and F is onto.
Theorem: In ZFC, if X is an infinite set, then for all n e N, there exists a Y c X such that there is function that map X onto Y.
Theorem: In ZFC, if X is an infinite set, then for all n e N, the cardinality of X is greater than n.
This is ZFC. If you want to create a consistent theory that is In opposition to ZFC, feel free. This, however, will NOT effect the validity of ZFC.