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Math Help - Boundary Question

  1. #1
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    Boundary Question

    Hi,
    I have this one other question and I think it requires a rigorous proof involving balls etc and I have no idea about how to go about it.

    Prove:  \partial \{ x \in \mathbb{R}^n : |x| < 1 \} = \{ x \in \mathbb{R}^n : |x|=1 \}

    Thanks again
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  2. #2
    Member HappyJoe's Avatar
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    What do you know about the boundary?

    For instance, do you know that Boundary(S) = Closure(S)\Interior(S)?

    If you do, then

    Boundary(open solid unit ball) = (the closed solid unit ball)\(the open solid unit ball) = the unit ball.

    Edit: Ah, you wanted a points-and-balls proof. I'll let this be anyway.
    Last edited by HappyJoe; September 30th 2010 at 03:29 AM. Reason: Didn't read the problem properly
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  3. #3
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    yaa, I needed a point-ball proof for this. Any help?

    Thanks a lot!
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  4. #4
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    I see that you have over twenty postings.
    By now you should understand that this is not a homework service
    So you need to either post some of your work on this problem or explain what you do not understand about the question.
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