On Wednesday, June 12, 2013 12:43:37 PM UTC-7, muec...@rz.fh-augsburg.de wrote: > On Wednesday, 12 June 2013 18:09:05 UTC+2, Zeit Geist wrote: > > > > >> Why prove anything else on that obviously broken basis? > > > > > You haven't proved that! You claim your algorithm is such a proof, But it fails. > > > > Then name a q or an n where my algorithm fails. Formal proofs based upon nonsense axioms are not acceptable, since I just disprove this nonsense formalism and the axioms which it is based upon. >
Choose any q e Q. For you algorithm to work, we have to be able find a step n_1 where that 1/2 of the rationals less than q are well-ordered, a step n_2 where 2/3 of the rations less than q are well-ordered, and so on for all numbers in form of n/n+1. This will never happen in you algorithm, so you never well-order all rationals in their order of magnitude.
Try this with an arbitrary list of natural numbers. For any natural m, we find the sequence of indices n_j for all j e |N. hence for |N, the switching algorithm should work.
If you feel this is not a necessary requirement for such an algorithm, PROVE it.