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Math Help - Power Sets

  1. #1
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    Power Sets

    Hey guys, I wanted to see if someone could check my work.

    Find  \mathcal{P}(\mathcal{P}(\left\{1\right\})) and its cardinality.

    \mathcal{P}(\left\{1\right\})=\left\{\oslash, \left\{1 \right\}\right\} then,

    \mathcal{P}(\mathcal{P}(\left\{1\right\}))= \mathcal{P}(\left\{\oslash, \left\{1 \right\}\right\}) = \left\{\oslash, \left\{1 \right\}, \left\{\left\{1 \right\}\right\}, \left\{\oslash, \left\{1 \right\}\right\}\right\}

    | \mathcal{P}(\mathcal{P}(\left\{1\right\}))| = 4

    correct?
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  2. #2
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    Re: Power Sets

    Quote Originally Posted by amthomasjr View Post
    Hey guys, I wanted to see if someone could check my work.
    Find  \mathcal{P}(\mathcal{P}(\left\{1\right\})) and its cardinality.
    \mathcal{P}(\left\{1\right\})=\left\{\oslash, \left\{1 \right\}\right\} then,
    \mathcal{P}(\mathcal{P}(\left\{1\right\}))= \mathcal{P}(\left\{\oslash, \left\{1 \right\}\right\}) = \left\{\oslash, \left\{1 \right\}, \left\{\left\{1 \right\}\right\}, \left\{\oslash, \left\{1 \right\}\right\}\right\}
    | \mathcal{P}(\mathcal{P}(\left\{1\right\}))| = 4 correct?
    Yes it i is correct.

    In fact if A is a finite set then \left| {\mathcal{P}(\mathcal{P}(A))} \right| = {2^{\left( {{2^{\left| A \right|}}} \right)}}
    Thanks from amthomasjr
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  3. #3
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    Re: Power Sets

    Thank you
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