Algorithm notation between two functions I have two functions,
$$ f = n^{1.6} $$
$$ g = n^{1.5} $$

I thought this is $ f=\theta(g) $, since $ f $ is asymptotically tight bound of $ g $, if $ n $ goes to infinity. However, the answer is  $ f = \omega(g) $. 
Can anyone explain why it is $ f = \omega(g) $ ?
Thanks in advance!
$\frac{f(n)}{g(n)} = \frac{n^{1.6}}{n^{1.5}} = n^{0.1}$ is unbounded. Hence, for any $c &gt; 0$ there is $n_0 \in \mathbb{N}$ such that $n^{0.1} &gt; c$ for all $n &gt; n_0$. As a result, for any $c &gt; 0$, we have $n^{1.6} = n^{0.1} \cdot n^{1.5} &gt; c n^{1.5}$ for all $n &gt; n_0$.

Notice this does not really make use of $1.5$ and $1.6$ other than $1.6 &gt; 1.5$. In fact, using the same method and the fact that $n^\varepsilon$ is unbounded for any $\varepsilon &gt; 0$, you can prove the more general bound $n^a \in \omega(n^b)$ for any $a &gt; b \ge 0$.