I've just encountered a weird statement regarding the BigOmega operator.
I should prove that the BigOmega operator isn't totally ordered. As a prove hint, I should show that there are two functions, say f(n) and g(n) such that:
$f(n)\ne \Omega(g(n))$ and $g(n)\ne \Omega(f(n))$
I read about the subject Total order in Wikipedia and I found out that the propery I'm missing (trying to prove that It doesn't exist) is "totality".
Although I know what I should prove It seems impossible.
Also I believe It won't be simple function such as: $n, n^2$ but something related to $log$.
Can someone please give me an hint?