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Math Help - Show A neither open nor closed

  1. #1
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    Show A neither open nor closed

    Show A neither open nor closed in (R^2) , where A={(x,o): -1<x<1}
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  2. #2
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    Re: Show A neither open nor closed

    Quote Originally Posted by rqeeb View Post
    Show A neither open nor closed in (R^2) , where A={(x,o): -1<x<1}
    Sorry to tell you that question is total nonsense.
    If x=0.5 the set (x,0) does not exist.

    Please reread and repost a correct question.
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  3. #3
    Super Member TheChaz's Avatar
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    Re: Show A neither open nor closed

    Quote Originally Posted by Plato View Post
    ...

    Please reread and repost ....
    Indeed.
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  4. #4
    Super Member TheChaz's Avatar
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    Re: Show A neither open nor closed

    Quote Originally Posted by rqeeb View Post
    Show A neither open nor closed in (R^2) , where A={(x,o): -1<x<1}
    Just use the definitions.
    Not open means there exists a point in R^2 such that the ball around this point (for any E > 0) contains a point not in A.
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  5. #5
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    Re: Show A neither open nor closed

    Quote Originally Posted by TheChaz View Post
    Indeed.

    but he Excersize in the book is written by this way:in {R}^2} show that:

    A=\{(x,0):\{-}\1<x<1\} is neither open nor closed.
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  6. #6
    Super Member TheChaz's Avatar
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    Re: Show A neither open nor closed

    Quote Originally Posted by rqeeb View Post

    but he Excersize in the book is written by this way:in {R}^2} show that:

    A=\{(x,0):\{-}\1<x<1\} is neither open nor closed.
    My first reply was a cheeky way of informing P that HE misread the question.

    My second reply is the direction you should go.
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