Big O notation

Big-O notation represents the upper bound of the running time of an algorithm. It gives the worst case complexity of an algorithm. ¹

O(g(n)) = { f(n): there exist positive constants c and n0
            such that 0 ≤ f(n) ≤ cg(n) for all n ≥ n0 }

It can also be said that g is "at most" f.