f(n) n 0 c 1 g(n) c 2 g(n) n O-notation † O, big Oh (upper limit) Notation : = . Intuition : f is smaller than g . When → ∞ : ≤ ∙ () . Definition : ∃ > , ∶ ∀ > ≤ ∙ () . Omega (lower limit) Notation : = . Intuition : f is larger than g . When → ∞ : ≥ ∙ () . Definition : ∃ > , ∶ ∀ > ≥ ∙ () . Theta (“as”) Notation : = . Intuition : f grows like g, i.e. between ∙ and ∙ . When → ∞ : ∙ () ≤ ≤ ∙ () . Definition : ∃ , > , ∶ ∀ ( > ) ∙ () ≤ ≤ ∙ () . o, little oh ‡ Notation : = . Intuition : f is a lot smaller than g . When → ∞ : ≪ () . Definition : →! () = . † More correctly, asymptotic notation. ‡ Onotation might not be asymptotically tight:2n 2 = O(n 2 ) is asymptotically tight, but 2n = O(n 2 ) is not. We use onotation (little oh) to indicate that our analysis is untight. n 0 f(n) cg(n) n n 0 f(n) cg(n) n