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Math Help - Closed and Unbounded set?

  1. #1
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    Closed and Unbounded set?

    Open and bounded sets seem to be abound (no pun intended), but I cannot think of any examples of closed and unbounded set, except for the trivial R and null sets.

    Do you know of any such sets?
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  2. #2
    Super Member Gamma's Avatar
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    The integers
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  3. #3
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    Quote Originally Posted by amoeba View Post
    Open and bounded sets seem to be abound (no pun intended), but I cannot think of any examples of closed and unbounded set, except for the trivial R and null sets.

    Do you know of any such sets?

    Any interval of the form [a,oo) or (-oo, a] is closed and unbounded.

    Tonio
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  4. #4
    Super Member Gamma's Avatar
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    the complement of any bounded open set is actually also closed and unbounded. Not all are gotten in this way though, as my first example demonstrates
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