title: O(log N) == O(1) - Why not?
body: <p>Whenever I consider algorithms/data structures I tend to replace the log(N) parts by constants. Oh, I know log(N) diverges - but does it matter in real world applications?</p>
  
  <blockquote>
    <p>log(infinity) &lt; 100  for all practical purposes.</p>
  </blockquote>
  
  <p>I am really curious for real world examples where this doesn't hold.</p>
  
  <p>To clarify:</p>
  
  <ul>
  <li>I understand O(f(N))</li>
  <li>I am curious about real world examples where the <strong>asymptotic</strong> behaviour matters more than the <strong>constants</strong> of the actual performance.</li>
  <li>If log(N) can be replaced by a constant it still can be replaced by a constant in O( N log N).</li>
  </ul>
  
  <p>This question is for the sake of (a) entertainment and (b) to gather arguments to use if I run (again) into a controversy about the performance of a design.</p>