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How to prove the set of all infinite subsets of $\mathbb{Q} = \mathfrak{c}$, if you first prove that the cardinality of the set of all finite subsets of $\mathbb{Q}$ is $\aleph_{0}$.

I know how to prove the finite subset of $\mathbb{Q}$ is $\aleph_{0}$ but hard to reach this problem

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    $\begingroup$ Do you know that the set of all subsets of $\Bbb N$ has cardinality $\mathfrak{c}$? $\endgroup$ – Brian M. Scott 2 days ago
  • $\begingroup$ I know the cardinality of the set of all real numbers is 2^N0 $\endgroup$ – RLOUIS 2 days ago
  • $\begingroup$ Is N you way of writing $\aleph$? $\endgroup$ – Hagen von Eitzen 2 days ago
  • $\begingroup$ Yes, N is ℵ. I just write n simply. $\endgroup$ – RLOUIS 2 days ago
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    $\begingroup$ Ok I got your point. Thank you for your help. $\endgroup$ – RLOUIS 2 days ago