Hi I have two questions, 1. A metric space is an ordered pair (M,d) where M is a set (which some authors require to be non-empty) and d is a metric on M, that is, a function [tex] d : M x M -> R [/tex] ------------From Wikipedia. http://en.wikipedia.org/wiki/Metric_space#Definition I just want to give my interpretation of what this says and if I'm reading this wrong could you correct my vocabulary/"mode of thought". :p This statement is saying that the generalized metric space "d" (say, a Euclidian or Cartesian Plane) maps (joins together in a workable way) sets M to the real numbers R. d - the metric space - is viewed as a function. 2. Is this the same way the Euclidian R x R plane is viewed when talking of "addition" in the following; [tex] + : (R x R) --> R [/tex] I would really appreciate it if you could explain where I'm wrong and what is correct.