I would like to know whether the number of infinity sets of different cardinalities is uncountable or countable. Is the proof simple? Thanks.
number of infinite sets with different cardinalities
7
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set-theory
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5The argument in http://math.stackexchange.com/questions/3061/large-sets-set-theory shows that the collection of cardinalities cannot form a set. If it did, you could take the powerset of their union. – 2010-08-22