Today we discussed in a lecture a very simple algorithm for finding an element in a sorted array using binary search. We were asked to determine its asymptotic complexity for an array of $n$ elements.
My idea was, that it is obvisously $O(\log n)$, or $O(\log_2 n)$ to be more specific because $\log_2 n$ is the number of operations in the worst case. But I can do better, for example if I hit the searched element the first time - then the lower bound is $\Omega(1)$.
The lecturer presented the solution as $\Theta(\log n)$ since we usually consider only worst case inputs for algorithms.
But when considering only worst cases, whats the point of having $O$ and $\Omega$-notation when all worst cases of the given problem have the same complexity ($\Theta$ would be all we need, right?).
What am I missing here?