Infinite Union operation of Formal Languages
Virtually every standard language class contains singleton languages, e.g. those languages containing exactly one word ($L_w = \{w\}$).

If a class containing every $L_w$ were closed under infinite union then it would contain any arbitrary infinite language $L$ since

$$
L = \bigcup_{w\in L} L_w
$$

More in general, we can write any language (finite or infinite) using an infinite union of singletons or empty languages.

$$
L = \bigcup_{w \in \Sigma^*} \{w\ |\ w\in L\}
$$

where $\{w\ |\ w\in L\}$ is $\{w\}$ when $w\in L$ and the empty language otherwise. (I wish set comprehensions had a standard notation for free and bound variables! Here, $w$ is free.)