Let $\Sigma = \{a, b\}$. Does $\varepsilon \in \Sigma^*$?

Question

I know it's really basic question but here it is:

Does the null word $\varepsilon$ belongs to the set of all words of an alphabet $\Sigma$?

For example, Let $\Sigma = \{a, b\}$. Does $\varepsilon \in \Sigma^*$?

Thanks in advance.

Answer 1

See definition for Kleene Star. The short answer to your question is 'yes'.

Answer 2

Usually. The zero, a neutral with respect to addition (concatenation) is a comfortable thing to have. This is the reason why we want it to be there.