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 from (x, y) to (z, w) is r" another way of saying the distance of (z, w) - (x, y) is r. Saying "the distance between (x, y) and (z, w) is r" is another way of saying "the distance from (x, y) to (z, w) is r and the distance from (z, w) to (x, y) is r".