title: Asymptotic notation properties proofs?
body: <p>I am trying to prove that if f(n) and g(n) are asymptotically positive functions, then:</p>
  
  <ol>
  <li><p>f(n) = O((f(n))^2)</p></li>
  <li><p>f(n) = O(g(n)) implies 2^(f(n)) = O(2^(g(n)))</p></li>
  <li><p>f(n) = O(g(n)) implies g(n) = O(f(n))</p></li>
  </ol>