Exercises
[0C3]Fixed \(k{\gt}0\), \(\varepsilon {\gt}0\) and a rational number \(x\), prove that there exist only finitely many rationals \(𝛼\) that can be represented as \(𝛼=m/n\) in order to satisfy the relation
\[ \left| x - \frac m n \right| ≤ \frac k{n^{1+\varepsilon }}\quad . \]Solution 1