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Homework Help: Power set

  1. Oct 4, 2013 #1
    1. The problem statement, all variables and given/known data

    How many elements does this set have?

    * P(P(∅))

    2. Relevant equations

    I know that if a set has n elements, then its power set has 2^n elements but i really want to know if (P(∅)) is just one element or not.

    Thanks in advance..
  2. jcsd
  3. Oct 4, 2013 #2


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    How many subsets does ##\emptyset## have?
  4. Oct 4, 2013 #3


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    Sure it is. The empty set has one subset. Itself. But remember P is the SET of subsets. So P(∅) isn't ∅. It's {∅}. There is a difference.
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