FOM: an "obvious" observation
martin_schlottmann at math.ualberta.ca
Fri Jan 23 20:34:20 EST 1998
There is an obvious solution to the problem of
ill-definedness of the intersection of e and pi:
One may add new constant symbols R, +, *,...
and the usual axioms for real numbers to ZFC,
and then use the usual set-theoretic definitions
of the reals only to show that this extension
is conservative. It is even possible to have
the real numbers as atoms in a conservative extension
of set theory (modifying the extensionality axiom
in a suitable way).
This formal proceedure seems as close as possible to the
usual informal way to deal with the problem of
"spurious" theorems like "pi intersect e = pi".
Martin Schlottmann <martin_schlottmann at math.ualberta.ca>
Department of Mathematical Sciences, CAB 583
University of Alberta, Edmonton AB T6G 2G1, Canada
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