For questions related to directed union. Directed union of set $H_i$($i∈I$) is defined as union of $H_i$ where for all $i,j∈I$,$\ i \geq j$ implies $H_i \supseteq H_j$.
Directed union of set $H_i$($i∈I$) is defined as union of $H_i$ where for all $i,j∈I$,$\ i \geq j$ implies $H_i \supseteq H_j$.
For example, union $ \bigcup_{n≧1} \Bbb{F}_q$ is directed because $n｜m$ implies $\Bbb{F}_{p^n}⊆\Bbb{F}_{p^m}$.
For more info, check this link.