Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Power set of a set of sets

  1. Sep 13, 2014 #1
    How are you supposed to go about putting together the power set of a set of sets such as
    X = {{1},{1,2}}

    What is the power set of X then? And what's the rule for calculating cardinality for the power set of a set that consists of elements which are sets such as the above? Because the set X to my understanding has 2 elements, both of which are sets... so the power set of X doesn't consist of only 4 elements, does it?

    There are:
    {}, {1}, {1,2}, {{1},{1,2}}

    Or is that really all?

    Please help clarify this to me, thanks so much.
  2. jcsd
  3. Sep 13, 2014 #2
    Yep, that's about it. You only care about finding the subsets of [itex]X[/itex] so the element [itex]a_i \in X[/itex] can be whatever.
  4. Sep 13, 2014 #3
    Actually, the singletons of X here are {{1}} and {{1,2}}. It's a subtle but important distinction.
  5. Sep 13, 2014 #4
    Oh yes, thank you gopher_p (and da_nang). I'm just glad it's not some crazy mix of inner and outer elements.
  6. Sep 14, 2014 #5
    If the iterated set notation confuses you, just do something like ##a = \{1\}, b = \{1, 2\}, X = \{a,b\}## and then at the end substitute back.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook