Definition:Theta Notation

Definition
Big-Theta notation is a 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. Then:
 * $$f(n) \in \Theta (g(n))$$ 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:
 * $$\lim_{n \to \infty} \frac{f(n)}{g(n)} = c$$, where $$0 < c < \infty$$.

If such a $$c$$ does exist, then $$f(n) \in \Theta (g(n))$$.