# Can a regular expression be any string from the language described by it? [closed]

Is it possible to have a regular expression from a language (that has strings of infinite length) which it describes ?

• Your question is not clear enough. Could you try rephrasing it, or perhaps add an example of what you mean? Sep 3 '20 at 7:56
• A language can be defined by a regular expression iff it is regular. Sep 3 '20 at 11:35
• No language contains strings of infinite length. Sep 3 '20 at 13:24
• Do you mean a language $L$ consisting of strings, at least one of which, $s_i$ interpreted as a regular expresssion exactly describes $L$? Sep 3 '20 at 15:10

Let $$\Sigma$$ be a (finite) alphabet and $$\epsilon$$ denote the empty word. A language is a subset of $$\Sigma^*$$, where $$\Sigma^*$$ is defined as $$\Sigma^* = \cup_{i=1}^{\infty} \Sigma^i$$, $$\Sigma^0 = \{ \epsilon \}$$, and $$\Sigma^i = \{xy : x \in \Sigma^{i-1}, y \in \Sigma\}$$ for $$i>0$$.
As you can see, a string of infinite length does not belong to any $$\Sigma^i$$ and therefore it belongs to neither $$\Sigma^*$$ nor to any of its subsets.