title: Are all NP problems also NP-complete?
body: <p>The definition of NP-complete is</p>
  
  <p>A problem is NP-complete if</p>
  
  <ol>
  <li>it belongs to class NP  </li>
  <li>all the other problems in NP polynomially transform to it</li>
  </ol>
  
  <p>So, if all other problems in NP transform to an NP-complete problem, then does that not also mean that all NP problems are also NP-complete?  What is the point of classifying the two if they are the same?</p>
  
  <p>In other words, if we have an NP problem then through (2) this problem can transform into an NP-complete problem. Therefore, the NP problem is now NP-complete, and NP = NP-complete. Both classes are equivalent.</p>
  
  <p>Just trying to clarify this up for myself.</p>