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Homework Help: Set question

  1. Oct 5, 2008 #1
    I know that the diameter for an interval [a,b] is defined as b-a

    but what is
    1. Diam of (-1,1]U(2,3)
    2.Diam of (1,1/2)U(1/4,1/8)U(1/16,1/32)U....

  2. jcsd
  3. Oct 5, 2008 #2


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    The diameter is defined as the diameter of the smallest interval that contains the set.
  4. Oct 5, 2008 #3


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    You obviously can't do that unless you know the definition of "diameter of a set or real numbers", not just the diameter of an interval. Fortunately, Dick has provided that.
  5. Oct 6, 2008 #4
    so if i am right

    1. Diam of (-1,1]U(2,3)=2+1=3
    2.Diam of (1,1/2)U(1/4,1/8)U(1/16,1/32)U....=1/2+1/4+1/16+....

    Is this correct?
  6. Oct 6, 2008 #5


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    The first one is correct, the second one is not. Did you notice that (1/4, 1/8), (1/16, 1/32), etc. are all SUBSETS of (1, 1/2)? What is (1,1/2)U(1/4,1/8)U(1/16,1/32)U....?
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