Big O, Big Omega, Theta - Slog #8

When we first learned about Big O, Big Omega and Theta this past few weeks, I often went into a blank state as to what the definitions were.
To sum it up,
Big O: O(g) = {f : N -> R+, ∃ c ∈ R+, ∃ B ∈ N, ∀n ∈ N, n ≥ B => f(n) ≤ c g(n)
Function f is bounded above by function g (constant factor of c).

Big Omega: Ω(g) = {f : N -> R+, ∃ c ∈ R+, ∃ B ∈ N, ∀n ∈ N, n ≥ B => f(n) ≥ c g(n)
Function f is bounded below by function g (constant factor of c).


Theta : Θ(g) = {f : N -> R+, ∃ c ∈ R+, ∃ B ∈ N,  ∀n ∈ N, n ≥ B => c1 g(n) ≤ f(n) ≤ c2 g(n) 
Note: It's basically the combination of Big O and Big Omega. 

Function f is bounded above by function g by a constant factor of c2 and bounded below by the same function with a constant factor of c1.