title: Pumping Lemma Assistance
body: <p>I recently had an assignment where I was asked to use pumping lemma to show that a language was not regular, and unfortunately got the wrong answer. </p>
  
  <p>The language to prove is non-regular is as follows:
  L = {a<sup>i</sup> b<sup>j</sup> c<sup>k</sup>: i = j or j = k}</p>
  
  <p>The definition of a pumping lemma that I was given is as follows:</p>
  
  <ol>
  <li>opponent picks m</li>
  <li>I want to pick w to contradict the pumping lemma. Use m to pick a string w ∈ L where |w| ≥ m</li>
  <li>opponent picks a decomposition of w subject to constraints. </li>
  <li>I try to pick an i so that the pumped string w<sub>i</sub> ∉ L. If found, L is not regular</li>
  </ol>
  
  <p>This subject has proven to be very difficult for me to understand and I feel like a complete airhead because of it, so a detailed explanation as to how I would properly apply a pumping lemma would be appreciated.</p>