Consider the set E := {k EN: kVn E Z}. Since qVn = p, we know that E is nonempty. Thus by the Well-Ordering Principle, E has a least element, say no.

Set x = no( Vn - mo). By (10), 0 < Vn - mo < 1. Multiplying this inequality by no, we find that

(11) 0< x < no.