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Math Help - Is this set theory statement true?

  1. #1
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    Question Is this set theory statement true?

    I think it is, but if someone could explain why or why not, it would be greatly appreciated.

    {4} ∈ P{6,4,3,2,5}

    Many thanks! I'm just getting my head around set theory.
    (The P is a power set symbol by the way!)
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  2. #2
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    Re: Is this set theory statement true?

    A\in P(B) means the same thing as A\subseteq B. Here, it is clearly true that \{4\}\subseteq\{6,4,3,2,5\}.
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  3. #3
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    Re: Is this set theory statement true?

    Your help is much appreciated, thank you. I never realised that it meant the same thing.
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  4. #4
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    Re: Is this set theory statement true?

    Quote Originally Posted by emakarov View Post
    A\in P(B) means the same thing as A\subseteq B.
    This is almost always true, but not quite. You can apply A\subseteq B in some cases when B is a proper class (and even if A is a proper class), but you can't take the power set of a proper class so A\in P(B) is not a valid statement. For example, it makes sense to say that the class of all ordinals form a subset of the class of all sets, and I can describe this in first-order logic without getting into paradoxes. However, it doesn't make sense to refer to the power set of the class of all sets (such a set does not exist).

    The important idea here is that the power set of a set X, is the collection of all X's subsets. So the members of P(X), when P(X) is a set, are precisely those things that are subsets of X.
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  5. #5
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    Re: Is this set theory statement true?

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