
Re: Problems with Infinity?
Posted:
Feb 25, 2013 11:58 AM


On Mon, 25 Feb 2013 08:48:05 0800 (PST), netzweltler <reinhard_fischer@arcor.de> wrote in <news:5da7d5eb57a043a8afba131c856173ce@he10g2000vbb.googlegroups.com> in rec.arts.sf.written,sci.math:
[...]
> If there is a horizontal infinite line, how do we assign > the origin?
Arbitrarily.
> 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, translationinvariant measure on the sigmaalgebra generated by the intervals. Thus, one the two of you choose a unit, the length of the interval between your origins is completely determined.

