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Math Help - Trying to understand specific condition of a set

  1. #1
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    Trying to understand specific condition of a set

    As requested:

    What I am asking, can {x} ∈ S and {x} ⊊ S, where x is a integer value and S is the set?

    The problem is:

    Find a pair set S such that {x} is an element of S and {x} is not included in S.

    My answer is, that this is not possible.

    From what I know:

    It is possible to have a set, A, and second set, B. Set B can be contained as an element of set A, however that also means that any element contained in set B is included in A. So A={B} while B={0, 3}, then A = {{0,3}}.

    Is my logic correct?

    --- Original
    Sorry, but I am a mature student taking this course Discrete Structures for the first time and am having a hard time trying to understand a particular situation dealing with sets.

    What I am feeling that I should know, to answer a particular question, is if a element can be apart of a set but not included within it. I clearly do not understand my notes, practice and reading.

    Can someone explain to me if this situation is possible or not?
    Last edited by navitude89; January 22nd 2013 at 01:55 PM.
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  2. #2
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    Re: Trying to understand specific condition of a set

    Quote Originally Posted by navitude89 View Post
    What I am feeling that I should know, to answer a particular question, is if a element can be apart of a set but not included within it. I clearly do not understand my notes, practice and reading.

    I have absolutely no idea what "if a element can be apart of a set but not included within it." could possibly mean.

    Can you clear up its meaning? Maybe give some examples.
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  3. #3
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    Re: Trying to understand specific condition of a set

    Quote Originally Posted by navitude89 View Post
    As requested:
    What I am asking, can {x} ∈ S and {x} ⊊ S, where x is a integer value and S is the set?

    The problem is:
    Find a pair set S such that {x} is an element of S and {x} is not included in S.
    My answer is, that this is not possible.

    Well that is better. But still this is confused: {x} is an element of S and {x} is not included in S.
    Does that mean \{x\}\in S BUT \{x\}\not\subset S~?

    Let \mathbb{Z} be the set of integers and \mathcal{P}(\mathbb{Z}) be the powerset of \mathbb{Z}( set of all subsets).

    If S=\mathbb{Z}\cup\mathcal{P}(\mathbb{Z}) then it has the property that (\forall n\in\mathbb{Z})[n\in S~\&~\{x\}\in S].

    Please do not edit a post to clarify. Post a new reply please.
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    Re: Trying to understand specific condition of a set

    " \{x\}\in S BUT \{x\}\not\subset S~" that is what I am trying to understand, however I do not understand anything that you have provided underneath.

    I am sorry for taking your time. Can you please close this thread.
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    Re: Trying to understand specific condition of a set

    Quote Originally Posted by navitude89 View Post
    " \{x\}\in S BUT \{x\}\not\subset S~" that is what I am trying to understand, however I do not understand anything that you have provided underneath. I am sorry for taking your time. Can you please close this thread.



    Let S=\{\1,\{2\}\} now \{2\}\in S but \{2\}\not\subset S because 2\notin S.
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