title: Proving Not Big Omega?
body: <p>I'm trying to prove that <em>k(n</em>^2) is not Big Omega of 2^<em>n</em> where <em>k</em> is a positive real number. I've looked at the negation of Big Omega. So I'm trying to find a <em>n</em> that's greater than or equal to some <em>n0</em> that also satisfies <em>k</em>(<em>n</em>^2) &lt; (2^<em>n</em>)<em>c</em> where <em>c</em> is a positive real number.</p>
  
  <p>I've tried choosing an n where n = 2^<em>n0</em> and this makes <em>n</em>^2 = 2^<em>n</em> but the issue is that for the inequality to work, <em>k</em> has to be less than <em>c</em> and I can't choose what <em>k</em> and <em>c</em> are. I've tried to solve for n in the inequality by taking the log of both sides but then I end up with log(<em>b</em>) - log(<em>c</em>) &lt; 2log(<em>n</em>) + <em>n</em>log(2) and I'm not exactly sure how to isolate for <em>n</em> in that case either. Any hints would be appreciated</p>