[FOM] Banach Tarski Paradox/Line

W.Taylor at math.canterbury.ac.nz W.Taylor at math.canterbury.ac.nz
Tue Nov 29 05:39:43 EST 2011

Quoting George McNulty <mcnulty at mailbox.sc.edu>:

> 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.

That is indeed amusing.  I also heard, possibly on this list, that one
of them, either Banach or Tarski, I forget which, was partly motivated
by the intent to convince the math world that AC was in fact unreasonable.
The math world by and large ignored this feature, clutching BT to its bosom
in a similar way to the Cantor set, space-filling curves and others,
(in spite of the different logical footing).  So Banach (or Tarski)'s hopes
came to nothing, and AC was retained.

Can anyone supply any detail on this apocryphum?

- wfct

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