In article <firstname.lastname@example.org>, Zeit Geist <email@example.com> wrote:
> 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 <firstname.lastname@example.org>, > > > email@example.com 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.
X need only be infinite if the set Y is a PROPER subset of X. > > 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.
In ZFC, if X is an Finite set, then for all n e N, there exists a Y c X such that there is function that map X onto Y. Namely whenever Y = X > > Theorem: In ZFC, if X is an infinite set, then for all n e N, the > cardinality of X is greater than n.
That one is both correct and meamingful. > > 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.
If you want to create a consistent theory other than ZFC, try ZF.
Standard mathematics is almost all compatible with ZF, with or without C. A very large part of standard mathematics is incompatible with WM's WMytheology. --