title: Using Closure Properties to prove Regularity
body: <p>Here's a homework problem:</p>
  
  <pre><code>Is L_4 Regular?
  Let L_4 = L*, where L={0^i1^i | i&gt;=1}.
  </code></pre>
  
  <p>I know L is non-regular and I know that Kleene Star is a closed operation, so my assumption is that L_4 is non-regular.</p>
  
  <p>However my professor provided an example of the above in which <code>L = {0^p | p is prime}</code>, which he said was regular by proving that <code>L*</code> was equal to <code>L(000* + e)</code> by saying each was a subset of one another (e in this case means the empty word).</p>
  
  <p>So his method involved forming a regex of <code>0^p</code>, but how I can do that when I essentially have one already?</p>