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Math Help - Generalized Union & Intersection

  1. #1
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    Generalized Union & Intersection

    Let Ai= {..., -2, -1, 0, 1, ...i}. Find.

    ( Ai)

    ( Ai)
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  2. #2
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    Please, please, learn to post in symbols? You can use LaTeX tags.

    [tex]A_i = \left\{ { \cdots , - 2, - 1,0,1,2, \cdots ,i} \right\}[/tex] gives A_i  = \left\{ { \cdots , - 2, - 1,0,1,2, \cdots ,i} \right\}.

    Review what you posted. Is the set A_i correct?
    It not bounded below but it is bounded above.
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  3. #3
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    Sorry about that. I will in the future. I was assigned this problem but we never went over it in any of the lectures. The book does not make it clear to me on how to solve for this.
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  4. #4
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    Please answer if the set A_i=\{\cdots,-2,-1,0,\cdots,i\} is correct.
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  5. #5
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    [Hello, lm6485!

    \text{Let }\,A_i\:=\: \{\hdots\,\text{-}2,\,\text{-}1,\,0,\,1,\,\hdots\, i\}

    \text{Find:}

    . . (a)\;\begin{array}{c} _n \\ \bigcup \\ ^{i\,=\,1}\end{array}\!\!A_i

    \begin{array}{c} _n \\ \bigcup \\ ^{i\,=\,1}\end{array}\!\!A_i \;=\; \{\hdots\,\text{-}2,\,\text{-}1,\,0,\,1\}

    . . . . . . \cup \;\{\hdots\,\text{-}2,\,\text{-}1,\;0,\,1,\,2\}

    . . . . . . \cup \;\{\hdots\,\text{-}2,\,\text{-}1,\;0,\,1,\,2,\,3\}

    . . . . . . . . . . . . . . . \vdots

    . . . . . . \cup \;\{\hdots\,\text{-}2,\,\text{-}1,\;0,\,1,\,2,\,3\,\hdots n\}


    \text{Therefore: }\;\begin{array}{c} _n \\ \bigcup \\ ^{i\,=\,1}\end{array}\!\!A_i \;=\; \{\hdots\,\text{-}2,\,\text{-}1,\,0,\,1,\,2,\,3,\,\,\hdots n\}




    (b)\;\begin{array}{c} _n \\ \bigcap \\ ^{i\,=\,1}\end{array}\!\!A_i

    \begin{array}{c} _n \\ \bigcap \\ ^{i\,=\,1}\end{array}\!\!A_i \;=\; \{\hdots\,\text{-}2,\,\text{-}1,\,0,\,1\}

    . . . . . . \cap \;\{\hdots\,\text{-}2,\,\text{-}1,\;0,\,1,\,2\}

    . . . . . . \cap \;\{\hdots\,\text{-}2,\,\text{-}1,\;0,\,1,\,2,\,3\}

    . . . . . . . . . . . . . . . \vdots

    . . . . . . \cap \;\{\hdots\,\text{-}2,\,\text{-}1,\;0,\,1,\,2,\,3\,\hdots n\}


    \text{Therefore: }\;\begin{array}{c} _n \\ \bigcap \\ ^{i\,=\,1}\end{array}\!\!A_i \;=\; \{\hdots\,\text{-}2,\,\text{-}1,\,0,\,1\}
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  6. #6
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    yes
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  7. #7
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    What would happen if instead of n it was \infty and the equation changed to {i, i +1, i + 2, ...}
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  8. #8
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    If this is a new question, please begin a new thread.
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