Operations with Asymptotic Notations I am wondering is anyone has something like a cheatsheet with all the operations between $O(n)$, $\Theta(n)$, $\Omega(n)$, $o(n)$, $\omega(n)$. For example, this is something I don't know how to solve:
$$\frac{\Theta(n)}{o(n)} =?$$
There are not many combinations and I was wondering if anyone could help me.
Classical resources: CLRS Introduction to Algorithms, 3d edition, pages 47, 1150,  Donald Ervin Knuth TAOCP, 1997, volume 1, page 107.
More formal good resource for such cheatsheet you can find  in Jeremy Avigad and Kevin Donnelly article.
And, at end, for non negative case, let me bring some well known properties:
$$ \begin{array}{l}O(f ) + O(g) = O(f + g) =O(\max(f,g))\\
C=Const. \Rightarrow C\cdot O(f) = O(C \cdot f) = O(f) \\
 O(f )  O(g) = O(f g) \\
O( O( f)) = O(f ) \\
 g \ne 0 \Rightarrow \frac{O(f)}{g} = O\left(\frac{f}{g}\right)
\end{array}
$$
For your case: $f \in \frac{\Theta(n)}{o(n)}$, if an only if $\lim\limits_{n \to \infty}f(n)=\infty$.