In article <email@example.com>, firstname.lastname@example.org wrote:
> On Wednesday, 12 June 2013 22:52:24 UTC+2, Zeit Geist wrote: > > > > > > That won't prove what Virgil stated. > > Either you can show a rational number q_i that cannot be well-orderd by size > with all its predecessors, or your claim is invalid. Divine interaction is > refuted.
Every finite ordered set is automatically well- ordered.
But let us see WM produce his alleged well-ordering the set of all rational integers with their standard ordering as rationals without divine intervention.
What us confusing WM is that he does not understand infinite sets, and assumes that everything that can be done with sets can only be done with finite sets.
For finite sets, ordered implies well-ordered. For infinite sets, there are ordered sets which are not well-ordered. So that for WM, imprisoned in the finiteness of Wolkenmuekenheim, his finite set of all rationals is well-ordered to begin with, and his argument about well ordering things adds nothing to his set of rationals.
But for those of us whose set of rationals is not forced to be finite, s WM's is, WM's arguments do not work at all outside Wolkenmuekenheim . --