The existence of a Metric Function allows the calculation of distance between any pair of elements in the set. Note, this could also include a pair where both elements in the pair are the same element.
If our set is a collection of numbers on a number line then we get the difference between element a and element b by simple subtraction and taking the absolute value.
A set with a metric is called a metric space.
We perk our ears up for this–is a metric space simpler than a vector space?
Appendix A
Yes, we have a possible project here: we have a question, what is the simplest (the way with least steps) to build subtraction? Part of me wonders if, by the time we are done, we will have everything that is present in a vector space.
Rob Sterling 