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Math Help - Proving a set closed

  1. #1
    Member thaopanda's Avatar
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    Proving a set closed

    Consider the metric space (R,d) with d(x,y) := |x - y| whenver x,y \in R. Show that the set N is closed.

    Help please...
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  2. #2
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    If x is not natural, there exists a natura number n such that

    n<x<n+1

    This clearly implies that there exists an open set containing x and not lying N.
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