Definition of Θ(f)

Θ(f) is the intersection of O(f) and Ω(f).

That means Θ(f) is the set of all functions that are bounded both above and below by functions roughly proportional to f.

Note that the function giving the bound above is almost certainly different from the function giving the bound below.

When we get even sloppier than usual, we might say Θ(f) is the set of all functions that are roughly proportional to f.