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I assume that the number of unique possible cardinalities that are uncountably infinite is either uncountable or countable because it is possible to take the powerset of each set, resulting in an uncountable number of elements; thus, there would be an infinite number of uncountable cardinalities. However, is this number of uncountable cardinalities going to be uncountable or countable?

Thanks!

will
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    In ZFC it is so large it is not even a set. – André Nicolas Jul 14 '15 at 01:24
  • There are uncountably many of them, but as André Nicolas notes, there is no such set. And that bears explaining too. I once encountered a quite intelligent mathematician who told me he didn't understand that idea. Maybe I'll see if that's here somewhere. – Michael Hardy Jul 14 '15 at 01:29

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