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

 Messages: [ Previous | Next ]
 Brian M. Scott Posts: 1,289 Registered: 12/6/04
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
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.

Date Subject Author
2/24/13 netzweltler
2/24/13 David DeLaney
2/25/13 netzweltler
2/25/13 Brian M. Scott
2/26/13 netzweltler
2/26/13 Wayne Throop
2/26/13 Brian M. Scott
2/27/13 netzweltler
2/27/13 David Bernier
2/27/13 Virgil
2/24/13 Frederick Williams
2/24/13 Frederick Williams
2/24/13 David DeLaney