What do these Big-O notations mean in context of comparison
In this context, this comparison means the subset of. Hence, $O(n\log n) &gt; O(n)$ means All members of $O(n)$ exist in $O(n \log n)$ as well or $O(n) \subset O(n \log n)$. For example, $f(n) = \sqrt{n} \in O(n)$ and $f(n) \in  O(n\log n) $ and $g(n) = n \log n \not \in O(n)$ and $g(n) \ \in O(n \log n)$.