p-adic absolute value ($|\cdot {|}_p$)

For a prime $p$, the $p$-adic absolute value on $\mathbb{Q}$ is $|x{|}_p=p^{-v_p(x)}$.

Every nontrivial absolute value on $\mathbb{Q}$ is equivalent either to the usual absolute value or to one $p$-adic absolute value.