title: In the context of Big O notation, what does asymptotic or asymptotically mean?
body: <p>I am trying to understand the words asymptotic and asymptotically. In other words, what do we really mean by a growth rate f(x)  being <strong><em>asymptotically</em></strong> greater than, less than, greater than or equal to, less than or equal to g(x) what does <strong>asymptotically</strong> really mean? I am <strong><em>not</em></strong> looking for a rehash of the question: "What is big O, big Theta and big Omega notation?"; just the meaning of the words asymptotic and asymptotically in this context. </p>
  
  <p>Example:</p>
  
  <p>"<strong>f(x) = O(g(x))</strong> (big-oh) means that the growth rate of f(x) is <strong><em>asymptotically</em></strong> less than or equal to the growth rate of g(x)."</p>
  
  <p>The above was taken from  this Stack Overflow page: <a href="https://stackoverflow.com/questions/471199/what-is-the-difference-between-%CE%98n-and-on">What is the difference between Θ(n) and O(n)?</a> </p>