I'm trying to figure out the implications of $\Omega$ in asymptotic analysis. Let's say I have a function $f(n)=\Omega(n)$. From my understanding, and Asymptotic analysis: difference between big O and big Omega limits?
this implies the following:
$\exists c>0$, such that $\exists n_0 $ s.t. $\forall n \ge n_0, \,\, f(n) \ge cn$
In some literature, I've heard this described as "f(n) cannot be bounded by a constant". I'd like to know why that is the case. To me $f(n)=\Omega(n)$ seems to imply the following:
$\nexists c >0$, such that $\exists n_0 $ s.t. $\forall n \ge n_0, \,\, f(n) < cn$.
...which to me means its performance cannot be bounded by a linear function of $n$. i.e. $O(n) < f(n)$. How does this imply $f(n)$ cannot be bounded by a constant? Can't we say something stronger?