For functions f(n) and g(n), we say that "f(n) is Big-O of g(n)" if
There exists a constant c > 0 there exists a constant n0 such that
for all n ≥ n0, 0 ≤ f(n) ≤ c * g(n)
We write f(n) = O(g(n)), but the "=" is not the usual meaning.
The intention is to allow us to say
Technically, 101,000,000*n is O(n), but programs with that running time is still very slow.