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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: 1,264
Registered: 12/6/04
Re: Problems with Infinity?
Posted: Feb 25, 2013 11:58 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Mon, 25 Feb 2013 08:48:05 -0800 (PST), netzweltler
<reinhard_fischer@arcor.de> wrote in
<news:5da7d5eb-57a0-43a8-afba-131c856173ce@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,
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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