FOM: David Ross's comment on the Banach-Tarski paradox
jbaldwin@uic.edu
jbaldwin at uic.edu
Thu Dec 11 03:36:15 EST 1997
This continuesthe Ross- Simpson thread on Banach-Tarski
Steve objected to lack of detail and contextl in the Ross post.
My understanding of Ross's comment was the following. There is no
Banach-Tarski paradox in dimension 2 (paradoxical decompositions of
the disk); there is a paradox in dimension 3. The fact that F_2
imbeds the group of Euclidean motions of R^3 provides an explanation
for this. It suggests that the Banach-Tarski paradox has a
geometrical as well a `purely foundational' component.
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