I am wondering in what ways we may quantify an irrational number's approximability.
This came up as I was reading about badly approximable numbers, which are those numbers $x$ such that
$$\liminf_{q \to \infty}q|qx-\{ qx\}| >0.$$
The number which the above limit converges to is known as the approximation constant, which might be described as a measurement of how closely we can approximate $x$ in denominators of growing size. Then I started reading about the Liouville-Roth irrationality measure, which is the greatest $u$ so that $|x - p/q| < 1/q^u$ for infinitely many pairs $(p,q)$ of positive integers.
Both of these numbers quantify irrationality, in some way.
So, as in my title: are there other ways we quantify approximability/irrationality of irrational numbers, or certain classes of irrational numbers (ie. quadratic numbers)?