On Mon, 25 Feb 2013 08:48:05 -0800 (PST), netzweltler <firstname.lastname@example.org> wrote in <news:email@example.com> in rec.arts.sf.written,sci.math:
> If there is a horizontal infinite line, how do we assign > the origin?
> How do we prove, that the distance in meter from the > origin I have chosen to the origin someone else (along > this line) has chosen can be counted?
By proving that Lebesgue measure is is the unique complete, translation-invariant measure on the sigma-algebra generated by the intervals. Thus, one the two of you choose a unit, the length of the interval between your origins is completely determined.