This notation provides a non-asymptotically tight lower bound for f(n). It can be simply written as, f(n) ∈ ω(g(n)), where
ω(g(n)) = {h(n) : ∃ positive constants c, n0 such that for any c > 0, n0 > 0, and 0 ≤ cg(n) < h(n),∀ n ≥ n0 }. This is unlike the Ω notation where we say for some c > 0 (not any). For example, 5n3 = Ω(n3 ) is asymptotically tight upper bound but 5n2 = ω(n3 ) is non-asymptotically tight bound for f(n).
Example of functions in ω(g(n)) include: n3 = ω(n2 ), n3.001 = ω(n3 ), n2 logn = ω(n2 )
An imprecise analogy between the asymptotic comparison of functions f(n) and g(n) and the relation between their values can be given as: f(n) = Ω(g(n)) ≈ f(n) ≥ g(n) f(n) = ω(g(n)) ≈ f(n) > g(n)