# Difference Between $n^{\Omega{(1)}}$ and $\Omega{(n)}$ [closed]

I am not sure about the difference between $$n^{\Omega(1)}$$ and $$\Omega(n)$$. It seems to me that the only difference is that $$n^{\Omega(1)}$$ can contain some sublinear functions, i.e., $$n^{\frac{1}{2}}$$, which is not the case for $$\Omega{(n)}$$. Is there any other differences between these two notations?

• You just explained what the difference is. – Yuval Filmus Nov 7 '19 at 19:28
• @YuvalFilmus So, $n^c \in \Omega(n), \forall 0<c<1$. And for the other, we have: $n^c \in n^{\Omega(1)}, \forall c \in \mathbb{R}$. – user777 Nov 18 '19 at 17:44
• In fact, $n^c = \Omega(n)$ iff $c \geq 1$. – Yuval Filmus Nov 18 '19 at 17:46