let $$p$$ be a prime in $$\mathbb{Z}$$. The $$p$$-adic order for $$\mathbb{Z}$$ is defined as $$v_p: \mathbb{Z}\rightarrow\mathbb{N}$$ $\displaylines{v_p(n) = \begin{cases} \max\{v\in \mathbb{N}: p^v | n\} & \text{if } n\neq 0 \\ \infty & \text{if } n=0 \end{cases} }$ The $$p$$-adic absolute value is defined as $$|\cdot|_p$$ $\displaylines{|x|_p=\begin{cases} p^{-v_p(x)} &\text{if } x\neq 0 \\ 0 &\text{if } x=0 \end{cases} }$ A metric space then can be defined by $\displaylines{d(x,y) = |x-y|_p }$