title: how to evaluate equality of big O notation?
body: <p>I've been asked a question that seems strange to me. Given the following two equalities, which is true, and which is false (or are they both either true or false)?</p>
  
  <ol>
  <li><p>O(n^2) = O(n^3)</p></li>
  <li><p>O(n^3) = O(n^2)</p></li>
  </ol>
  
  <p>To me, this question seems absurd, since O(f(n)) just means that for some time function T(n), lim as n -> infty of T(n) &lt;= c * f(n).</p>