Hello,

Let G be the system of subsets A \subset \mathbb{R} such that A can be written as
A = (a1 , b1 ] ∪ (a2 , b2 ] ∪ · · · ∪ (an , bn ]
where -\infty\le a_1 \le b_1 \le ... \le a_n \le b_n \le \infty

Why (if we consider A_1, ..., A_n \in G)

\cup_{i\ge 0} A_i \notin G ?

thanks