EDB — 0XW

Exercises

1. [0XW]Difficulty:*.Show, for every \(a/b∈ℚ\) with \(a,b\) coprime and \(b\) not divisible by \(p\), there exists \((x_ n)_ n⊆ ℤ\) such that \(|x_ n-a/b|_ p→_ n 0\). Note that the assumption is necessary.

   Solution 1

   [0XX]↺↻

   We proved that \(ℤ\) is dense in the disk \(\{ x∈ℚ, |x|_ p≤ 1\} \).