$S=\bigcup_{n \in \mathbb N}\left[\frac{1}{2^n},8-\frac{1}{n}\right)$
I wrote out the first few intervals and see that this converges to the open interval $(0,8)$. So given that I'm trying to find the union of these intervals, I believe the union of intervals is $\left[\frac{1}{2},7\right]$
If this is true, then
$\text{infS}=\frac{1}{2}$
$\text{minS}=\frac{1}{2}$
$\text{supS}=7$
$\text{maxS}=7$
Did I got about this the correct way?