big "Oh" notation : Number Theory #BIG #oh #NOTATION #: #Number #Theory
big "Oh" notation : Definition : Suppose g(x) > 0 for all real values x ≥ a and f(x) is a real valued function such that f(x)/g(x) is bounded for x ≥ a . Then we say that " f(x) is of large order g(x) " or " f(x) is of order g(x) ". In this case , we write f(x) = O(g(x)) ( we read f(x) is big Oh of g(x). Equivalently , we can say that f(x) = O(g(x)) if there exists M > 0 such that | f(x)/g(x) | ≤ M for all x ≥ a , or |f(x) | ≤ M |g(x)| or for all x ≥ a . Note : i) f(x) = h(x) + O g(x) means that f(x) - h(x) = O g(x) ⇒ | f(x) - h(x) | ≤ M g(x) for some M > 0. ii) Suppose f(t) = O g(t) for t ≥ a ⇒ | f(t) | ≤ M g(t) for t ≥ a and for some M > 0. ...