So I have this question to prove a statement:
I don't need to know how to prove it, just that in my mind this makes no sense and I think it should rather be that $\Theta(n)\subset O(n)$.
My understanding is that $O(n)$ is the set of all functions who do no worse than $n$ while $\Theta(n)$ is the set of all functions that do no better and no worse than n.
Using this, I can think of the example of a constant function say $g(n)=c$. This function will surely be an element of $O(n)$ as it will do no worse than $n$ as $n$ approaches a sufficiently large number.
However, the same function $g$ would not be an element of $\Theta(n)$ as g does do better than $n$ for large $n$... Then since $g \in O(n)$ and $g \not\in \Theta(n)$, then $O(n)\not\in\Theta(n)$
So is the question perhaps wrong ? I've learnt it is dangerous to make that assumption and usually I have missed something, I just can't see what it might be in this case.
Any thoughts ? Thanks a lot..