# Meaning of L* if L is a language

I can't find anywhere the meaning of $$L^*$$, given that $$L$$ is a language. I know $$^*$$ means repetition, for example $$0^*$$ = $$\{ \epsilon, 0, 00, 000, \dots \}$$. Or if $$A$$ is an alphabet $$A^*$$ are all the possible words.

Does $$L^*$$ mean the language whose words are the concatenation of the words of $$L$$?

For example if $$L=\{ 01^n \mid n>0 \}$$

then is $$L^* = \{ 01^{n_1}01^{n_2} \dots \mid n_1>0, n_2>0, ... \}$$?

• $L^\ast = \bigcup_{i=0}^\infty L^i$, where $L^i = \{ w_1 \cdots w_i \mid w_1, \ldots, w_i \in L \}$. See also here. – dkaeae Jul 3 at 13:05
Given a language $$L$$, let $$L_0 = \{\epsilon\}$$ and, for $$i\geq 1$$, let $$L_i = \{w_1\circ \dots\circ w_i \mid w_j\in L \text{ for each } j\}$$, where $$\circ$$ denotes concatenation. Then the Kleene closure of $$L$$ is the language $$L^* = \bigcup_{i\geq 0} L_i$$.