The second episode on metric spaces is focussed on a concept derived from the convergence of sequences of real numbers. Knowing what distances between elements in metric spaces are, we immediately realise that we also know, when two elements of a metric spaces are close. Namely, when the metric evaluated at those elements is small. Thus, we introduce convergence of sequences in metric spaces to some limit element by asking for the metric evaluated at the sequence elements and the limit form a null sequence of real numbers. We illustrate the versatility of the developed ideas by looking at an example in image processing.