For p a given prime number, define the p-adic norm | * |p as
follows on Q: Given q in Q, we can write it as a product q =
(p^m)(a/b) with a,b integers which are not divisible by p, and m an
integer which is uniquely determined by q (check that m is indeed
uniquely determined by q). Then define |q|p = p^(-m).
Check that Q with distance dp(q1,q2) = |q1 - q2|p is a metric
space (here q1-q2...