[tsimionescu]

Note that "the amount of steps / operations / time an algorithm will take" is not in general a mathematical function, as for the same input size, different inputs will give different numbers of steps. For bubble sort for example there doesn't exist a function f(n) = number of steps bubble sort will take for an input of size n. There does exist a function best_case_complexity(n) = number of steps bubble sort will take for the best input of size n; and a function worst_case_complexity(n) = number of steps bubble sort will take for the worst input of size n.

Then, we can say best_case_complexity(n) = Theta(n), and worst_case_complexity(n) = Theta(n^2). We can also define the set of all functions representing the number of steps bubble sort will take for input of a certain "shape" of size n. We can then indeed say that any function in this set will be <= worst_case_complexity(n) and >= best_case_complexity(n), so this set will indeed be a subset of Omega(n) and of O(n^2).