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Math Help - Polygon Connected Sets

  1. #1
    Member aldrincabrera's Avatar
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    Smile Polygon Connected Sets

    ,.hello there,.,i need some hint for this agen,.,

    Let S={all (x,y) with x and y rational numbers}
    Show that the complement is a polygon connected set. is it an open set??


    thnx
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Re: Polygon Connected Sets

    Quote Originally Posted by aldrincabrera View Post
    ,.hello there,.,i need some hint for this agen,.,

    Let S={all (x,y) with x and y rational numbers}
    Show that the complement is a polygon connected set. is it an open set??


    thnx
    I assume that you mean polygonally line connected. Here's a way to think about it, isn't the set equal to \displaystyle \bigcup_{x\in\mathbb{R}-\mathbb{Q}}\left(\{x\}\times\mathbb{R}\cup\text{x-y axis}\right)\cup\bigcup_{y\notin\mathbb{Q}}\left( \mathbb{R}\times\{y\}\cup\text{x-y axis}\right)? Draw that out and I think you'll have your answer.
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  3. #3
    Member aldrincabrera's Avatar
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    Re: Polygon Connected Sets

    .,.amm,.,.thnx sir,.,but i got confused in drawing it,.
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