In article <email@example.com>, firstname.lastname@example.org wrote:
> On Saturday, 22 June 2013 23:38:57 UTC+2, Zeit Geist wrote: > >>> Is that a true statement? > > > > Of course, if the plane is a plane. > > > Would that Boing or Sescna? > > Products from BOEING or CESSNA I would call aeroplanes. > > > But really, not sure what you mean. Do you mean if the plane is a Euclidean > > Plane? > > I don't know other "planes" in pure geometry. > > But with respect to your ulterior motive: The existence of non-Euclidean > geometries is in no relation with the question whether anybody in reality can > well-order all real numbers.
That depends on which axiom system one assumes. Not all axiom systems allow a proof that the reals can be well ordered.
For example,the system ZF + AD does not allow such a proof. --