[Solved]: How do you prove Sigma Star is regular

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I noticed in another answer on this forum

Note that the languages ∅, {ϵ} and Σ* are regular.

How do you prove Sigma Star is regular.

Asked By : gatech-kid

Answered By : David Richerby

It's easy to design a DFA that accepts $\Sigma^*$. Or, if your definition of regular languages is in terms of regular expressions, then the regular expression $(a_1\mid\dots\mid a_k)^*$ matches $\Sigma^*$, where $\Sigma = \{a_1, \dots, a_k\}$.

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