# Generalized Union & Intersection

• Oct 12th 2010, 08:24 AM
lm6485
Generalized Union & Intersection
• Oct 12th 2010, 08:37 AM
Plato
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 $\displaystyle A_i = \left\{ { \cdots , - 2, - 1,0,1,2, \cdots ,i} \right\}$.

Review what you posted. Is the set $\displaystyle A_i$ correct?
It not bounded below but it is bounded above.
• Oct 12th 2010, 09:25 AM
lm6485
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.
• Oct 12th 2010, 09:37 AM
Plato
Please answer if the set $\displaystyle A_i=\{\cdots,-2,-1,0,\cdots,i\}$ is correct.
• Oct 12th 2010, 12:51 PM
Soroban
[Hello, lm6485!

Quote:

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

$\displaystyle \text{Find:}$

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

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

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

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

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

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

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

Quote:

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

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

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

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

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

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

$\displaystyle \text{Therefore: }\;\begin{array}{c} _n \\ \bigcap \\ ^{i\,=\,1}\end{array}\!\!A_i \;=\; \{\hdots\,\text{-}2,\,\text{-}1,\,0,\,1\}$
• Oct 13th 2010, 09:41 AM
lm6485
yes
• Oct 13th 2010, 11:02 AM
lm6485
What would happen if instead of n it was $\displaystyle \infty$ and the equation changed to {i, i +1, i + 2, ...}
• Oct 13th 2010, 11:06 AM
Plato