title: Uniform cost search and completeness
body: <p>In my AI textbook, the following has been said about uniform cost search:</p>
  
  <blockquote>
    <p>Therefore, it will get stuck in an infinite loop if there is a path with an infinite sequence of zero-cost actions.</p>
  </blockquote>
  
  <p>I understand this part.</p>
  
  <p>However, it also mentions:</p>
  
  <blockquote>
    <p>Completeness is guaranteed provided the cost of every step exceeds some small positive constant.</p>
  </blockquote>
  
  <p>I don't understand how the positive constant helps. Even if this condition was satisfied, an infinite path would still cause the algorithm to not find a possible solution.</p>
  
  <p>Could someone explain this part?</p>