I seem to have trouble with getting my head around a metric space.
I read the definitition of a metric which states that it is a function describing the distance between two points in a set, that is the shortest distance.
Then a metric space is a set where the notion of distance between elements of the set is defined.
I do not get how the distance between two points in a set can not be defined, so I was looking for an example of a non-metric set.
Unfortunately i could not find any, could someone shed some light on this issue for me?