On Saturday, June 22, 2013 12:34:12 PM UTC-7, muec...@rz.fh-augsburg.de wrote: > On Saturday, 22 June 2013 20:21:28 UTC+2, Virgil wrote: > > > > The axiom was not assumed as the typical nonsense of present day "logic" but > as true. > > > > > > > How or why it was assumed is of no consequence to the issue of whether anyone not assuming it would claim the reals to be well-orderable. > > > > The question is whether the reals can be well-ordered, whether it can be done. Zermelo's "proof" is not important, but should only be the foundation, like the Theorem of Pythagoras says something for every rectangular triangle. The calculation has to be excuted by arithmetic and geometry. > > But in this case. it cannot be executed! >
What about the statement,
"In a plane, given a line, l, and a point, p, such that p is not on l; then there exists exactly one line, k, such that k is parallel to l and p is on k.