Banach-Tarski paradox
IDEA OF TAKING APART AN OBJECT AND CONSTRUCTING TWO IDENTICAL COPIES OF IT
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<
mathematics> It is possible to cut a solid ball into finitely
many pieces (actually about half a dozen), and then put the
pieces together again to get two solid balls, each the same
size as the original.
This
paradox is a consequence of the
Axiom of Choice.
(1995-03-29)