In p-adic mathematics, what is the advantage of using Teichmuller representatives over using just the numbers 0,1,2,...,p-1 ?

In either case, the norm is the same. In either case, all the points are in the center.

Is is fair to say: "Teichmuller representives, just like the digits 0,1,2,...,p-1 , are just names of elements that are different in name but in no other characteristic. Although p-adic arithmetic seems more complex using Teichmuller representatives, more advanced mathematics is easier and more robust."

notjust like 0,1,..,p-1 (when p > 2). – KConrad Mar 4 '11 at 4:26