Is Cauchy a 1 N sequence?
Definition We say that a sequence of real numbers {an} is a Cauchy sequence provided that for every ϵ > 0, there is a natural number N so that when n, m ≥ N, we have that |an − am| ≤ ϵ. Example 1 Let x be a real number and tn(x) be the nth truncation of its decimal expansion as in Lectures 2 and ...