User:Blackbombchu/Sandbox/Definition:Distance

In R2, for any (x, y), for any real number r, saying the distance of (x, y) is r is another way of saying there is exactly one distance function and that function assigns r to (x, y). For any two points in R2, (x, y) and (z, w) and any real number r, saying the distance between (x, y) and (z, w) is r another way of saying the distance of (z, w) - (x, y) is r.