FOM: Re:precursors of Cantor

charles silver silver_1 at
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

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