Definition:Big-Omega Notation

=Definition= Big-Omega notation is a one type of order notation for typically comparing 'run-times' or growth rates between two growth functions.

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

$$f(n){\in}{\Omega}(g(n))$$ iff, $${\exists}c>0,k{\geq}0$$, such that $${\forall}n>k, f(n){\geq}cg(n)$$

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

Another method of determining the condition is the following limit:

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