title: Is there any function that is in o(1)?
body: <p>A colleague of mine has asked me a question: Is the set <code>o(1)</code> (<a href="http://en.wikipedia.org/wiki/Big_O_notation#Related_asymptotic_notations">little o notation</a>) empty?</p>
  
  <p>My question is: Is <code>o(1)</code> an empty set? If not, is there a program that has <code>o(1)</code> time complexity?</p>
  
  <p>Reminder, definition of little-o by <a href="http://syedwaqarahmad.webs.com/documents/t._cormen_-_introduction_to_algorithms_3rd_edition.pdf">Cormen</a>: </p>
  
  <blockquote>
    <p>A function <code>f(n)</code> is said to be in <code>o(g(n))</code> if for any positive
    constant <code>c&gt;0</code>, there exists a constant <code>n0 &gt; 0</code> such that <code>0 &lt;=f(n) &lt; cg(n)</code> ,  for all <code>n&gt;= n0</code>.</p>
  </blockquote>
  
  <p>Intuitively, if <code>f(n)</code> is in <code>o(g(n))</code> if it is in <code>O(g(n))</code>, but this bound is NOT tight.</p>