## Stable infinite union

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