R Hansen says: >I guess I felt that Neighbor was asking - What do you mean by ?set of points?? What are these points? If they have no width then how can they add up to make a line, even an infinite number of them? And so forth. I was just thinking that he might be able to apply what you wrote regarding ?sets" to "points on a line" if he understood "points on a line" better. The best model I am aware of to do that with is the set of real numbers. I suppose that you could make headway with just the rational numbers, as long as the student has given them sufficient thought, as a set.
Well, where I would proceed to next, with even getting into numbers per se (which Neighbor seemed to want to avoid) would be to look at the other subset, the one that does *not* include the cut point C. Then see what we can say about that set and the points that are its elements, without treating it as a number system overtly, just cull out the properties that seem needed to talk about whatever.