- Given the set of functions defined on a subset in $\mathbb{R}$ and taking values in $\mathbb{R}$, I was wondering if $O$ as in $f \in O(g)$ is a total partial order? By total, I would like to know if every two functions can be compared by $O$? Is it acting like $\geq$ on $\mathbb{R}$?
- How about $\Omega$, $\Theta$, $o$, $\omega$ and $\sim$? Are they acting like $\leq$, $==$, $>$, $<$ and $==$ respectively?
For definitions, see Wikipedia. Thanks and regards!