 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2006/e/e1/a/solution

In a metric space, a Cauchy sequence has arbitrarily small distances between all sufficiently late terms:

\forall ε > 0 \exists N \forall m, n \geq N : d (x_{m}, x_{n}) < ε .

This condition compares terms to each other and does not assume that a limit exists in the space.

 New to topics? Read the docs here!