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Homework Help: A new thought and a problem |P(A)| = 1?

  1. Sep 9, 2011 #1
    1. The problem statement, all variables and given/known data


    P(A) = power set of A (in my book it is funky looking P, someone tell me how to read it and what it is)

    What is |A| and |P(A)|?

    a) A = [tex]\o[/tex]

    Book say that

    |A| = 0, and |P(A)| = 1

    Why?

    P(A) = {\o} I know that this is one thing (or one element), but the symbol represents empty set meaning nothing so

    {\o} = {{no elements}} = {}

    SO Why isn't |P(A)| = 0?

    EDIT: \o is supposed to be that symbol that looks like the greek letter phi, but I don't know why it isn't showing
     
  2. jcsd
  3. Sep 9, 2011 #2

    Dick

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    You can also write phi as {}. {} contains no elements. It's the empty set. |{}| means the number of elements in {}. That's 0. P({}) is the set of all subsets of {}. There's only one, {}. So P({})={{}}. It contains one element {}. So |{{}}|=1.
     
  4. Sep 10, 2011 #3

    SammyS

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    Do you mean this [itex]\mathcal{P}[/itex] ? use \mathcal{P}

    For [itex]\emptyset\,,[/itex] use \emptyset, although, \o does work for some implementations of LaTeX.
     
  5. Sep 10, 2011 #4
    Yes thank you lol, now I am wondering the heck is \o lol
     
  6. Sep 10, 2011 #5
    But {} is nothing
     
  7. Sep 10, 2011 #6
    Actually why is the empty set is a subset of A anyways?
     
  8. Sep 10, 2011 #7

    vela

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    It's not nothing. It's a set containing no elements. You can't just erase the curly brackets willy-nilly.
    It's because it's true that every element of the empty set is an element of A. Or to put it in a way that may be a little clearer, {} doesn't contain an element that is not also in A.
     
  9. Sep 10, 2011 #8

    Dick

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    Try it this way. The empty set is like a bookcase containing no books. It's not nothing, it's still a bookcase.
     
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