In article <email@example.com>, Zeit Geist <firstname.lastname@example.org> wrote:
> On Wednesday, June 12, 2013 12:39:58 PM UTC-7, muec...@rz.fh-augsburg.de > wrote: > > On Wednesday, 12 June 2013 17:59:40 UTC+2, Zeit Geist wrote: > > > > > > Every configuration can be well-ordered by size. This implies there is > > > > no q that stays outside the well order. > > > > > > > > > Every finite one can, but not the entire set of Q. > > > > > > > > I prove that all elements of Q can be well-ordered by size. You cannot > > disprove it, because you cannot find any element that stays outside, can > > you? > > > > You proved nothing! > You proposed an algorithm, > But never showed that it conclusively does what you say. > > > > > > Any finite set of real numbers can be well- according to magnitude. > > > Infinite ones, not necessarily. > > > > > > > > Either find a q that stays outside of the well-order by size.
There is a clear counter-example to your claim above: each S_n is well-ordered but the union, being the set of all negative integers is not since it does not have a smallest/first-in-order member. --