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In the context of regular expressions is Ø* = Ø? and why?

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    Please try to add more context. – 2017-02-10
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    What does that symbol mean here? – 2017-02-10
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    @copper.hat That's the [Kleene star](https://en.wikipedia.org/wiki/Kleene_star) operator, which is standard notation in this context. (Incidentally: to the OP, your question is answered in the third example at the page linked in my previous sentence!) – 2017-02-10
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    @jeff I appreciate your wanting to answer, but the context is regular expressions, the question was answered below correctly. – 2017-02-10
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    @jdoe okay then :) – 2017-02-10

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$\Sigma^*$ is the set of all finite strings, each of whose terms is from $\Sigma$ . . . so the answer is no!

The empty string, $\epsilon$, is an element of $\emptyset^*$: all of its terms are in $\emptyset$, because there aren't any. This is an instance of a more general phenomenon: universal statements always hold of the emptyset. For example, every element of the emptyset (or term of the emptystring) is a pink elephant.

And it's not hard to see that $\epsilon$ is the only element of $\emptyset^*$ (any string other than $\epsilon$ has at least one term - well, we can't have that here!). So $\emptyset^*=\{\epsilon\},$ which is not the same thing as $\emptyset$ (for the same reason that $\{\emptyset\}\not=\emptyset$; see e.g. here).

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    Thank you! This makes tons of sense, and in hind-site I should have realized. Great answer. – 2017-02-10