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Math Help - doubt

  1. #1
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    doubt

    Respected sir,
    I hava the following doubt. please clarify my doubt.


    let x belongs to {1}.
    <=> x belongs to any one of the subsets of {1}.
    <=> x=1 or x belongs to {}.
    But generally every body will write
    x=1 <=> x belongs to {1}.
    But for to use <=> we should write:
    x belongs to{1} and x does not belongs to {}.
    Why dont every one write like this.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ksssudhanva View Post
    Respected sir,
    I hava the following doubt. please clarify my doubt.


    let x belongs to {1}.
    <=> x belongs to any one of the subsets of {1}.
    Because this statement is not true. \{ 1 \} has only one element. That is to say that \emptyset \notin \{ 1 \}. \emptyset is indeed a subset of \{ 1 \}, but no element of this set is equal to \emptyset because the empty set is not listed as one of the set members.

    -Dan
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by ksssudhanva View Post
    Respected sir,
    I hava the following doubt. please clarify my doubt.


    let x belongs to {1}.
    <=> x belongs to any one of the subsets of {1}.
    <=> x=1 or x belongs to {}.
    But generally every body will write
    x=1 <=> x belongs to {1}.
    But for to use <=> we should write:
    x belongs to{1} and x does not belongs to {}.
    Why dont every one write like this.
    Because for all x in A, A!={}, x is not in {}.

    RonL
    Last edited by CaptainBlack; August 11th 2007 at 08:45 AM.
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