1. Let f and g be real-valued functions. Assume that f and g are nonnegative, that is, for all real numbers n, f (n) ≥ 0 and g(n) ≥ 0. We say that f (n) is Big-O of g(n), written f (n) = O(g(n)), if...

1. Let f and g be real-valued functions. Assume that f and g are nonnegative, that is, for all real numbers n, f (n) ≥ 0 and g(n) ≥ 0. We say that f (n) is Big-O of g(n), written f (n) = O(g(n)), if there exist positive constants c and n⁰
such that f (n) ≤ cg(n) for all n ≥ n₀.

2. Let f (n) be a nonnegative, real-valued function such that f (n) = amnm + am_1n^m_1
+ … +a1n + a0, wherein ai’s are real numbers, am ≠ 0, n ≥ 0, and m is a nonnegative integer. Then, f (n) = O(nm).