Cauchy sequence in $\mathbb{Q}_p$ implies its p-absolute value is cauchy in $R$

Question

Actually, I don't understand why $\{ a_{n}\} \in \mathbb{Q}_{p}$ is cauchy implies $|a_{n}|_{p} \in \mathbb{R}$ is cauchy. Could anyone give me a hint for understand this?

Answer 1

Here’s a Hint: use the reverse Triangle Inequality, that $|a-b|\ge|a|-|b|$. This says that $|a_m-a_n|\ge|a_m|-|a_n|$. That should give it to you.