I need to prove or contradict:$$|O(2n) - O(n)|=O(n)$$
I try:
$$\\f(n)=1.5n\in O(2n),g(n)=0.25n\in O(n),h(n)>0\in O(n) : \\
|1.5n - 0.25n|=h(n)\\1.h(n)=1.25n \in O(n)\\
but: 2. h(n)=-1.25n \notin O(n)$$
Is that true?