So I have a problem that's asking me to compute the intersection of all sets $S(k)$ such that
$$ S(k) = \left(\frac{k-1}{k}, \frac{2k+1}{k}\right], k \ge 1 $$
My answer is $(1,2)$, but the book's answer is $(0,2)$. Maybe I'm just dumb, but I do not understand why the book's answer would be correct.
Any help would be appreciated.