[FOM] A new definition of Cardinality.
meskew at math.uci.edu
Thu Nov 26 16:16:09 EST 2009
In my opinion, having that every two sets are comparable in size is
good. It is a natural idea and very fruitful. I think anyone should
see it as an advantage of choice. On the other hand, the existence of
a nonmeasurable set of reals and a paradoxical decomposition of a
sphere I think should be seen by anyone as a disadvantage of choice.
The way I see it, you can weigh the advantages and disadvantages and
make your own decision. But I don't think you should be able to make
your decision and then claim that everything that follows is good and
everything that follows from the opposite decision is bad. There must
be some biting of bullets either way.
On Wed, Nov 25, 2009 at 2:16 PM, Vaughan Pratt <pratt at cs.stanford.edu> wrote:
> 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.
> Vaughan Pratt
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