How can I find the sup, inf, min, and max of $\bigcup\left[\frac{1}{n}, 2-\frac{1}{n}\right]$ $$\bigcup\left[\frac{1}{n}, 2-\frac{1}{n}\right]$$
I'm not sure how to get started with this one.  When I graph the two functions I see they intersect at the point $(1,1)$, which I take to be the union of the set.  
But how do I use this information to obtain the inf, min, sup, and max, particularly if there is only one element in the set?  Is $1$ the inf, min, sup and max?

The union consists of all real numbers $x$ such that $\frac{1}{n}\leq x\leq 2-\frac{1}{n}$ for some natural number $n$. This is a much larger set than just the single point $\{1\}$. For instance, taking $n=2$ shows that all real numbers $x$ with $\frac{1}{2}\leq x\leq \frac{3}{2}$ are included in the union.
Some leading questions to get you started: what happens to $\frac{1}{n}$ as $n\to\infty$, and what does this tell you about the union?
