Besides the 'continuous' which I don't fully understand the term. It's all the time said that arbitrary gates can only be estimated but not necessarily be accurate. I don't understand the claim. So what if it's continuous? So do I have, uncountable many points on the Bloch sphere and I could certainly get from one to any other point using just two rotation gates.
So my question is basically, simply why aren't two rotation matrices enough not just to approximate but even to accurately calculate any arbitrary transformation so they could be described as a 'universal set' (If you need control you can add CNOT but that's it!). I mean, all you gotta do is playing around with the rotations so you switch a vector state on the surface sphere from one to another. That's enough, why not?
(I know there you may be required to use CNOT for some control qubits, but we usually define the universal set to be a bigger one, why? And why we just approximate and don't get exact or arbitrarily close to the answer?)