FOM: David Ross's comment on the Banach-Tarski paradox jbaldwin at
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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