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Homework Help: Set notation (union and intersection)

  1. Oct 21, 2009 #1
    1. The problem statement, all variables and given/known data

    Find simpler notation for the two sets:

    [tex]A= \bigcup^{\infty}_{j=0}[j,j+1][/tex]


    [tex]B= \bigcap_{j \in Z}(R minus\ (j,j+1))[/tex]

    2. Relevant equations

    3. The attempt at a solution

    Not really sure what it means by "simpler notation"...

    Does [tex]A=R[/tex] since the union of [j,j+1] would eventually cover the whole interval?

    And [tex]B=Z[/tex] because the intersection of R minus (j,j+1) would only leave the integers because it is an open interval.
    Last edited: Oct 21, 2009
  2. jcsd
  3. Oct 21, 2009 #2


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    For A you have the right idea, but is it really every single real number? Consider what the smallest element in A is.

    For B, it looks like each of the sets that you are taking the union of is


    Shouldn't each of those sets be a subset of B then?
  4. Oct 21, 2009 #3
    Sorry, for B, it should be an intersection. I just fixed it.

    For A, I think it should be R+ since it starts at [0,1]..
  5. Oct 22, 2009 #4


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    R+ sounds good, for B wirite it in terms of its complement and use the fact an intersection of complements is then complement of the union
  6. Oct 22, 2009 #5


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    re-read your first post - sounds about right for the 2nd one
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