None of this has anything to do with Banach-Tarski.
I guess that this is where we disagree.
Cantor was not the first to be seriously concerned with the
fundamentals
of the infinite/infinitesimal. The axiom of choice is a major link
between Banach-Tarski and the axiomatic set-theoretic calculus of the
continuum.
--
Chuck Britton Education is what is left when
britton@ncssm.edu you have forgotten everything
North Carolina School of Science & Math you learned in school.
(919) 416-2762 Albert Einstein, 1936