# Thread: Generalized Union & Intersection

1. ## Generalized Union & Intersection

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

( Ai)

( Ai)

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

$$A_i = \left\{ { \cdots , - 2, - 1,0,1,2, \cdots ,i} \right\}$$ 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.

3. 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.

4. Please answer if the set $A_i=\{\cdots,-2,-1,0,\cdots,i\}$ is correct.

5. [Hello, lm6485!

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

$\text{Find:}$

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

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

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

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

. . . . . . . . . . . . . . . $\vdots$

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

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

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

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

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

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

. . . . . . . . . . . . . . . $\vdots$

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

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

6. yes

7. What would happen if instead of n it was $\infty$ and the equation changed to {i, i +1, i + 2, ...}

8. If this is a new question, please begin a new thread.

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