[FOM] A new definition of Cardinality.
pratt at cs.stanford.edu
Wed Nov 25 17:16:28 EST 2009
Monroe Eskew wrote:
> It is worth pointing out that your definition still has a disadvantage
> if you don't assume choice. Without choice, not all cardinalities are
> comparable. If they were then all cardinalities in your sense would
> be comparable to a cardinality that contains a Von Neumann ordinal,
> but from this you could derive choice. (It is nice to have a linear
> order on set sizes.)
How is this a disadvantage? Those uncomfortable with choice are surely
going to be uncomfortable with the idea that every set has an injection
either to or from the set of reals.
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