Question

p-adic Analytic Number Theory:
I would greatly appreciate any help with this, it's driving me crazy.
For \(r>0\) let \(B_{r}(x)\) denote \((y \in Q_{p} : |y - x|_{p} < r) \) i.e. the open ball in the p-adic numbers with centre \(x\) and radius \(r\). Show that for two balls \(B_{r_{1}}(x_{1})\) and \(B_{r_{2}}(x_{2})\) either they are disjoint or one contains the other.

Answer 1

@hero @TuringTest , do any of you guys have any ideas please?

Answer 2

@Fellowroot