The context. For any real number $x$, let's define the quantity $$\mu(x):=\sup\left\{\mu\in\mathbb R_+\, \text{there is an infinity of rationals $p/q$ such that}\ \left\vert x-\frac pq\right\vert<\frac 1{q^{\mu}}\right\},$$ and let's call it the irrationality measure of $x$. We know that $$...