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# Big Omega (Ω) and Big Thera (θ) Notation

## Asymptotic Notations

Asymptotic notations are used to represent the complexities of algorithms for asymptotic analysis. These notations are mathematical tools to represent the complexities. There are three notations that are commonly used.

## Big Omega Notation

Big-Omega (Ω) notation gives a lower bound for a function f(n) to within a constant factor.

We write f(n) = Ω(g(n)), If there are positive constants n0 and c such that, to the right of n_{0} the f(n) always lies on or above c*g(n).

Ω(g(n)) = { f(n) : There exist positive constant c and n0 such that 0 ≤ c g(n) ≤ f(n), for all n ≤ n_{0}}

## Big Theta Notation

Big-Theta(Θ) notation gives bound for a function f(n) to within a constant factor.

We write f(n) = Θ(g(n)), If there are positive constants n0 and c_{1} and c_{2 }such that, to the right of n_{0} the f(n) always lies between c_{1}*g(n) and c_{2}*g(n) inclusive.

Θ(g(n)) = {f(n) : There exist positive constant c_{1}, c_{2} and n_{0} such that 0 ≤ c_{1} g(n) ≤ f(n) ≤ c_{2 }g(n), for all n ≥ n_{0}}

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