f(n) is in O(g(n)) means there exist constants c > 0 and n_0 ≥ 0 such that for all n ≥ n_0,

**Big-O is an upper bound:** f(n) ≤ c · g(n) for some positive constant c and all sufficiently large n. Equality is Theta (tight) the ≥ inequality is Omega (lower bound) strict > is not how the bound is defined.