- #1
Demon117
- 165
- 1
Homework Statement
For integers m and n, let d(m,n)=0 if m=n and d(m,n) = 1/5^k otherwise, where k is the highest power of 5 that divides m-n. Show that d is indeed a metric.
Show that, in this metric, the set Z of integers is totally bounded and perfect.
The Attempt at a Solution
I frankly do not know where to begin with this proof. I guess my first question is, what must I show precisely?