title: Usage of Big O for speedup comparison
body: <p>From an (excellent) <a href="https://mathematica.stackexchange.com/a/58762/19553">answer</a> at another SE site a statement was presented which I reacted on: "X is roughly O(10^4) times faster than Y".</p>
  
  <p>From the context it was obvious that the meaning was something along the lines of "X is roughly 4 orders of magnitude faster than Y", but this got me thinking: What exactly does such a Big O statement mean? I was sure at first sight the two were not equivalent, but thinking about it I cannot get my head around what it means exactly.</p>