Past exam of the Probability, statistics and options II course of the University of Oxford / 2010 / E / E4 / b

A sequence is Cauchy ifThe comparison is between sufficiently late terms, without presupposing a limiting point in the space.

A metric space is complete if every Cauchy sequence of its points converges to a point of that same space. The requirement on the location of the limit distinguishes, for example, $\mathbb{R}$ from its incomplete subspace $\mathbb{Q}$.