Define Big-O notation

Question

Big-O notation: If f(n) and g(n) are functions of a natural number n, we write

f(n) is O(g(n))

and we say f is big-O of g if there is a constant C (independent of n) such that f(n) ≤ Cg(n) for all suciently large n, or, more precisely, such that for some constant N we have f(n) ≤ Cg(n) for all n ≥ N.

With care, we can also use the big-O notation in equations. We might write

f(n) = O(g(n)) or f(n) = g(n)+O(h(n));