I should prove or give a counterexample for:
$\partial (\bigcup_{i \in \mathbb{N}} A_i) \subset \bigcup_{i \in \mathbb{N}} (\partial A_i)$
Where $\partial$ is the boundary and (X,d) is a metric space with $A_{i} \subset X $ for each $i \in \mathbb{N}$
I cannot make up a counterexample for finite sets $A_{i}$ but I think there might be one for infinite ones, or am I wrong?