A couple of questions:

  1. When choosing $C$ do I have to choose an integer? I see nothing in my definitions preventing fractions, but I haven't seen any in anything I've looked up, either
  2. Given $f(x)=O(g(x))$, is there anything preventing me from choosing $f(x)=g(x)$ such as $f(x)=x^2$ and $g(x)=x^2$?
  • $\begingroup$ 1) Please ask only one question per post. 2) Please make clear what the problem is. You already state that the definitions seem to agree with you; if you are just after confirmation, ask your teacher. 3) Question 2 only makes limited sense; why would you "choose" $f$ and $g$? Usually they exist and you claim/prove the relationship that is denoted by "$\in O(.)$". $\endgroup$ – Raphael Sep 15 '14 at 10:58
  1. Usually the definition of $O$ allows for $C$ to be any positive real number.

  2. That's a perfectly valid choice.

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