Definition:Theta Notation

Definition
Big-Theta notation is a one type of order notation for typically comparing 'run-times' or growth rates between two growth functions. Big Theta is a stronger statement than Big-O and Big-Omega.

$$Suppose: f,g$$ are two functions.

$$f(n){\in}{\Theta}(g(n))$$ iff, $$(f(n){\in}O(g(n)){\and}(f(n){\in}{\Omega}(g(n))$$

This is read as "f(n) is big-theta of g(n)".

Another method of determining the condition is the following limit:

$$lim{_{n->\infty}}{\frac{f(n)}{g(n)}} = c < {\infty}$$, where $$0<c<{\infty}$$. If such a c does exist, then $$f(n){\in}{\Theta}(g(n))$$.