Question: I am having a hard time comprehending what exactly the questions are asking. My thinking so far is that I am trying to find a family of subsets that satisfy the union and intersections of for example $x > n^2.$
So if i took $A\_{1}$ I would get all real numbers greater than $1$ for the union, and for the intersection wouldn't it just be $\{\emptyset\}$ since as we go to infinity there will never be a set that has the same values?

If there are any resources online that I could read that would explain this or if someone can guide me in the right direction that would be awesome.

Work out $\cup\_{n=1}^{\infty}A\_{n}$ and $\cap\_{n=1}^{\infty} A\_{n},$ where $A\_{n}$ is defined as follows for $n \in \Bbb N.$

1. $A\_{n}=\{ x\in \Bbb R \mid x > n^2 \}.$
2. $A\_{n}=\{ x\in \Bbb R \mid \frac{1}{n^2}<x<\sqrt{2}+\frac{1}{n}\}.$
3. $A\_{n}=\{ x\in \Bbb R \mid -3n<x<\frac{1}{n^2}\}.$

Answer: 
$\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\\$$\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\\$=$\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\\$
Let $A=\left[ \begin{matrix} 0 & 0 \\
1& 0 \end{matrix} \right].$