I am doing homework to practice for my midterm exam and cannot answer this question. I need to decide whether or not this statement is true of false and either give a proof or counter example.
For this particular question, I am leaning more towards saying it is false as the question does not really follow the definition of Big Omega. However, how do I come up with a counterexample for this? Can anyone show me how to do this question?
Let $g$ and $h$ be any functions from $\mathbb{N}$ to $(0,\infty)$. Then $g(n)\in\Omega(h(n))$ implies there is some $N\in\mathbb{N}$ such that $g(n)\geq h(n)$ for all $n\geq N$.
Any help would be much appreciated.