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Topic: Problems with Infinity?
Replies: 14   Last Post: Feb 27, 2013 4:22 PM

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Brian M. Scott

Posts: 1,289
Registered: 12/6/04
Re: Problems with Infinity?
Posted: Feb 25, 2013 11:58 AM
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On Mon, 25 Feb 2013 08:48:05 -0800 (PST), netzweltler
<> wrote in
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.

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