[FOM] Banach Tarski Paradox/Line
mcnulty at mailbox.sc.edu
Mon Nov 28 12:05:27 EST 2011
The only thing I might add is that Tarski was amused by the contrast:
Banach's proof that there are no paradoxical decomposition in dimensions
one and two relied on the Hahn-Banach Theorem, which in turn relied on
the Axiom of Choice. So the result of no paradoxical decompositions was
a fragile a result as the result giving paradoxical decompostion---from
the point of view of those who doubted the Axiom of Choice.
Somewhere (in Wagon's book?) I heard there was a proof of no paradoxical
decompositions in dimensions 1 and 2 without choice, but I do not
On 11/27/2011 04:27 PM, pax0 at seznam.cz wrote:
> Is the Banach Tarski paradox provable for the unit real interval;
> i.e. is there a possibility for duplicating [0,1].
> If not, where is the obstacle?
> Jan Pax
> FOM mailing list
> FOM at cs.nyu.edu
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