title: Why isn't the class of Turing-Recognizable languages closed under Complement?
body: <p>I'm studying Turing Machines and I've already showed how Turing-Decidable is closed for the operations of Union, Intersection, Concatenation, Complement and Kleene Star. Next I did some demonstrations to show how T-Recognizable languages are closed for Union, Intersection, Concatenation and Kleene Star.</p>
  
  <p>Now I'm trying to answer a question to show why the classe of T-Recognizable languages are not closed for the operation of Complementation, but I cannot understand it. Could someone please explain this?</p>
  
  <p>Thanks</p>