If $X$ is the intersection of all the intervals $(1-\frac{1}{n^2},1+\frac{5}{n^3}]$ for $n=1$ to infinity, what is the minimum, maximum, supremum and infimum of $X$?
If $Y$ is the intersection of all the intervals $(1-\frac{1}{n^3},1+\frac{1}{n})$ for $n=1$ to infinity, what is the minimum, maximum, supremum and infimum of $Y$?
I have $X=(1,1]$ and $Y=(1,1)$ which I think are both empty? My guess is that there is no minimum or maximum for either $X$ or $Y$ . I don't know whether the infimums/supremums are $1$ or whether you say they are infinite or something. I'm not sure what to do with the empty sets.