0
$\begingroup$

I've started to learn regular expressions in one of my classes

I know that a* is infinite, which leads me to believe that a*∅ is not infinite, since concatenating any language by a empty set is just empty set, similar to multiplying by zero. Is this line of thinking correct?

$\endgroup$
1
  • 2
    $\begingroup$ Yes, your argument is correct. Any set concatenated with the empty set gives the empty set. $\endgroup$ – Fabio Somenzi Feb 16 '17 at 3:45
1
$\begingroup$

Yep, that's correct. An element of $a^*\emptyset$ would be a concatenation of an element of $a^*$ with an element of $\emptyset$. But there aren't any elements of $\emptyset$! So there is no way to build an element of $a^*\emptyset$, and it is empty.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.