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Math Help - Power Set

  1. #1
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    Power Set

    Find the power set of each of the following sets.
    a. 0
    b. {0}
    c. {0,{0}}

    What is the cardinality of each of the power sets you just found?
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  2. #2
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    Is this your question?
    Find the power set of each of the following sets.
    a.  \emptyset b. \{ \emptyset \} c. \{ \emptyset, \{ \emptyset\}\}
    What is the cardinality of each of the power sets you just found?

    If so, what do you think about the (a) part?
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  3. #3
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    Quote Originally Posted by captainjapan View Post
    Find the power set of each of the following sets.
    a. 0
    b. {0}
    c. {0,{0}}

    What is the cardinality of each of the power sets you just found?

    Patrick Suppes in his book ,AXIOMATIC SET THEORY on page 47 gives a good proof of :


    ...........P(Φ) = { Φ }, Φ being the empty set.


    After that we have that:


    P({Φ}) = { Φ.{Φ}} AND :

    P({φ,{Φ}}) = {Φ,{Φ},{{Φ}},{Φ,{Φ}}}
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  4. #4
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    Yes that's my question. Sorry for the misunderstanding.

    Find the power set of each of the following sets.
    a. b. c.
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