p-adic numbers (with p=5 here).
For this problem, we're dealing with the set of integers with the metric where is the highest power of of 5 that divides .
I'm trying to either prove or disprove that this is a complete space. I know I have to either come up with a Cauchy sequence of integers that does not converge in the integers with respect to , or show that every Cauchy sequence in the integers converges in the integers with respect to . I'm just not seeing which one is the case. Does anyone have a hint to get me going in the right direction?