Exercise 4, § 7

Give an example of an infinite sequence $(F_n)$ of vector subspaces of a vector space $E$ such that $\operatorname{codim}\left(\bigcap_n F_n\right) > \sum_n \operatorname{codim}(F_n)$. (Take $\operatorname{codim}(F_n) = 1$ for all $n$ and use Exercise 3 (d).)