EDB — 0C5

Exercises

1. [0C5]Prove that for every rational \(m/n\) you have

   \[ \left| \sqrt{2} - \frac m n \right| {\gt} \frac 1{4n^ 2}. \]

   We obtain that the set \(A = ⋃_{m∈ℤ,n ∈ \mathbb {N}^*} \left( \frac m n - \frac 1{4n^ 2} , \frac m n + \frac 1{4n^ 2}\right)\) is an open set that contains every rational number, but \(A≠ℝ\).

   Solution 1

   [0C6]↺↻