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What is the cardinality of the power set $\mathcal P\left(S\right)$ where $S$ is a set of $15$ elements?

I think the power set is a set of all the subsets of a given set or $2^n$. So would the cardinality of this set be $2^{15}$ or $32,768$?

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    $\begingroup$ Yes, that is correct. $\endgroup$ – Henno Brandsma Oct 26 '14 at 18:07
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Yes, the cardinality of the power set $\mathcal P(S)$ of a set $S$ is given by $2^n$, and so in your case, by $2^{15}$.

Note: There is a difference between a set, and its cardinality. The power set $\mathcal P(S)$ itself is the set of all subsets of $S$, whereas $2^n$ is the number of these sets (which are the elements) in $\mathcal P(S).$

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    $\begingroup$ Wow you've helped me in every level of my math classes. From pre-calculus, to integral calculus and linear algebra, to now this class! As always, thanks for your help! $\endgroup$ – hax0r_n_code Oct 26 '14 at 18:09
  • $\begingroup$ You're always welcome, inquisitor. $\endgroup$ – Namaste Oct 26 '14 at 18:15

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