Is this Language regular?

Question

$L = \Bigl \{ \Sigma^*  \Bigr \}$

Comments

Are you really asking about $\{\Sigma^*\}$, or did you mean $\Sigma^*$?

The answer will be different for both cases.

---

Yes Dr. Agarwal,  I got your point. Actually this question came in my mind. Your comment below(in answers section) made it clear. The correct answer for this question is : "L is not a Language."

Answer 1

Definition- language is a set of strings, here it is a set of set of strings.

But even Σ is not defined here and if I take ∑=a, a character and not an alphabet set, then we get a language.

eg: Let  ∑={a,b},Then,  ∑^∗={ϵ,a,b,aa,ab,ba,bb,…}. However, { ∑*} = {{ϵ,a,b,aa,ab,ba,bb,…}}

So, its like this L={ ∑^∗}

L = { language }

so, L is not even a language .

Comments

No. A string is a sequence of characters. Now, if $\Sigma$ is a set of characters, $\Sigma^*$ becomes a set of strings (language), but $\{\Sigma^*\}$ becomes a set of set of strings, which by definition is not a language.

---

As Arjun sir explains it, $\Sigma$ is a set. $\Sigma^*$ is a language, that is, a set of strings.

Let $\Sigma = \{a,b\}$,

Then, $\Sigma^* = \Bigl \{\epsilon,a,b,aa,ab,ba,bb,\ldots \Bigr \}$.

However, $\{ \Sigma^* \} = \Biggl \{ \Bigl \{\epsilon,a,b,aa,ab,ba,bb,\ldots \Bigr \} \Biggr \}$

And that is not even a language, since it is not a set of strings.

---

So, L={Σ^∗} this statement is invalid ??

language = { language }

Answer 2

Yes the language is regular.

We can create automata for that language.