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From: dmn@uvacs.UUCP
Newsgroups: net.math
Subject: Re: Axiom of Choice
Message-ID: <980@uvacs.UUCP>
Date: Sun, 9-Oct-83 15:45:36 EDT
Article-I.D.: uvacs.980
Posted: Sun Oct  9 15:45:36 1983
Date-Received: Wed, 12-Oct-83 22:35:27 EDT
Lines: 11

References: tekmdp.2286

Some time ago I attended a talk in which the proof of the Banach-Tarski
theorem was presented.  One step in the partitioning of the pea sphere
involves picking points from the sphere that aren't *close* to each other
in real space (using the Axiom of Choice) and calling this collection
a *piece* of that sphere.  A mathematical point has no volume so that
to my mind the counter-intuitive result follows more from the way this
so called piece is defined than from the fact that the Axiom of Choice
is used in the proof.
  David Nicol (uvax/dmn)