FOM: Re:precursors of Cantor
charles silver
silver_1 at mindspring.com
Fri Jun 14 12:29:50 EDT 2002
Sorry, let me clarify my question. I know Schroder-Bernstein. Call
two sets A and B EquiSize (ES) iff there's a 1-1 f'n from A to B and vice
versa. Suppose set theory does not have Cantor's usual def'n for sets
being "the same size." Now, one would have to prove that there's also a
1-1 *onto* f'n from A to B to prove Cantor's original notion. What I'm
really wondering about is whether the proofs of *this* direction (from ES)
would be better ("more intuitive," "more natural," etc.) or worse (etc.)
than the usual proofs of Schroder-Bernstein (when starting out with Cantor's
usual def'n). Furthermore, I'm wondering whether "adjusting" set theory
this way would have other desirable/undesirable effects.
Charlie Silver
More information about the FOM
mailing list