A metric space is a set of elements coupled with a function \delta such that given any x, y, and z in the set of elements the following hold:

- Positivity: \delta(x,y) >= 0
- Triangle-Inequality: \delta(x,y) + \delta(y,z) \leq \delta(x,z)
- Symmetry: \delta(x,y) = \delta(y,x)
- Identity: \delta(x,y) = 0 iff x = y