As far as I understand, $2^{\aleph_0}$ is the cardinality of the real numbers (and whether this equals $\aleph_1$ is the continuum hypothesis). But would $2^{2^{\aleph_0}}$ be of a higher cardinality than the cardinality of the real numbers?
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asked May 26, 2016 at 13:58
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1$\begingroup$ The powerset of the continuum is bigger than the continuum $\endgroup$– user_of_mathMay 26, 2016 at 13:59
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1 Answer
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Yes, you are right. Generally, we have $2^\kappa > \kappa$ for any cardinal number $\kappa$.
