Is $2^{2^{\aleph_0}}$ a higher cardinality than $2^{\aleph_0}$?

Question

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?

Answer 1

Yes, you are right. Generally, we have $2^\kappa > \kappa$ for any cardinal number $\kappa$.