A set of points together with a function, d, called a metric function or distance function. The function assigns a positive real number to each pair of points, called the distance between them, such that:
3. For any two points x and y, not necessarily distinct,
d(x,y) = d(y,x).
4. For any three points x, y, and z, that are not necessarily distinct,
d(x,z) <= d(x,y) + d(y,z).