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

Problem Detail: 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 $(a_1middotsmid a_k)^*$ matches $Sigma^*$, where $Sigma = {a_1, dots, a_k}$.
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