That's not a feature of O; that's simply a feature of leaving stuff out. O is a simplification of a function, but says nothing about how to construct the funct

That's not a feature of O; that's simply a feature of leaving stuff out. O is a simplification of a function, but says nothing about how to construct the function. You need to have your (implicit) computational model before you can start counting critical operations, whether you describe it or not. This is actually somewhat important, since almost everyone has agreed on a model that, among other things, considers random access, multiplication, hashing, and even explicitly O(log log n) operations to take constant time. It's one of the many reasons why people make incorrect proofs about P=?NP. edit: If you meant that the simplification abstracts away implementation details like 3n^2+42 vs 2n^2+n, you're right, that's valuable. But I still argue that you ascribe it too much value when it comes to underspecifying your computational model.