Show that a set of open intervals can be formed by the countable union of sequences of rationals.

Question

I recently decided to get into probability theory. I am following Jacod and Protter, "Probability Essentials".

One of the first theorems (T.2.1) uses the following :

Let $C$ denote all open intervals in $\mathbb R$. Let $(a, b)$ be part of $C$. Consider a sequence of rationals strictly decreasing to $a$ and a sequence of rationals strictly increasing to $b$ ( $a_n$ and $b_n$ ).

$$(a , b) = \bigcup_{n=1}( a_n , b_n]$$

I am a bit rusty on this. But why is the interval $( a_n , b_n]$ closed on the right ?

Thanks in advance.