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Math Help - dense

  1. #1
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    dense

    Hi--

    is the set {1/n | n \in N} dense in [0,1].
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by Chandru1 View Post
    Hi--

    is the set {1/n | n \in N} dense in [0,1].
    A set is dense in [0, 1] if the set unioned with its limit points gives you [0, 1]. Now, there is nothing between 1/2 and 1 in your set; your set intersect trivially with (1/2, 1). So, well, does there exist a sequence in your set which has limit, say, 3/4?
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  3. #3
    Member mohammadfawaz's Avatar
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    simply ask yourself the following:
    is every number in [0,1] either a limit point of the given set or in it?
    if yes, then you have a dense set in [0,1]
    else, you don't
    in this case, the example given (3/4) does not satisfy any of the two conditions. (why?)
    Conclude.
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