FOM: Re: precursors of Cantor
neilt at mercutio.cohums.ohio-state.edu
Fri Jun 14 10:47:42 EDT 2002
On Fri, 14 Jun 2002, charles silver wrote:
> What would happen if a one-to-one correspondence were defined as a
> one-to-one map in both directions instead of being one-to-one plus onto in
> only one direction?
Clarification needed: do you mean something like
the Fs are in 1-1 correspondence with the Gs
there is a 1-1 map of all the Fs into the Gs
there is a 1-1 map of all the Gs into the Fs ?
In that case, wouldn't the Schroeder-Bernstein theorem yield the existence
of a 1-1 map from the Fs onto the Gs ?
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