= Infinite intersection of regular languages
<Regular languages> are closed under finite <intersection>, but not countably infinite <intersection>. Indeed, for any <formal language> $K\subseteq\Sigma^*$ over a finite <alphabet>, let $L_i$ contain every <word> of length at least $i$, together with the members of $K$ of length less than $i$. Each $L_i$ is a <regular language>, since its exceptional short part is a <finite language>, and $\bigcap_{i\geq1}L_i=K$. Thus every <formal language>, including one that is not a <regular language>, can arise in this way.
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