Definition:Big-Omega
Definition
Big-Omega notation is a type of order notation for typically comparing 'run-times' or growth rates between two growth functions.
Let $f, g$ be two functions.
Domain and range of $f$ and $g$ to be specified: reals?
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Then:
- $\map f n \in \map \Omega {\map g n}$
- $\exists c > 0, k \ge 0: \forall n > k: \map f n \ge c \map g n$
This is read as:
- $\map f n$ is big omega of $\map g n$.
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Another method of determining the condition is the following limit:
- $\ds \lim_{n \mathop \to \infty} {\frac {\map f n} {\map g n} } = c > 0$
where $0 < c \le \infty$.
If such a $c$ does exist, then:
- $\map f n \in \map \Omega {\map g n}$
The below into its own page
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To say that $\map f n \in \map \Omega {\map g n}$ is equivalent to:
- $\map g n \in \map \OO {\map f n}$
where $\OO$ is the big-O notation.