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Besides the usual set operations like union, intersection etc., concatenation can be applied to languages:
if both <math>S</math> and <math>T</math> are languages, their concatenation <math>S \cdot T</math> is defined as the set of concatenations of any string from <math>S</math> and any string from <math>T</math>, formally <math>S \cdot T = \{ s \cdot t \mid s \in S \land t \in T \}</math>.
Again, the concatenation dot <math>\cdot</math> is often omitted for
The language <math>\{\varepsilon\}</math> consisting of just the empty string is to be distinguished from the empty language <math>\{\}</math>.
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