On Jan 28, 2014, at 11:18 AM, Neighbor <email@example.com> wrote:
> Having a straight-line AB we can cut this into two straight-lines AG and GB by means of a point (let it be G). > Now, suppose I ask you, when we separate the two lines, on what straight-line the point G will be? And since this is one point (which is initially on AB), it will either be on AG or GB, for one point cannot be on both straight-lines, BEING ONE. Let it remain on AG, then what will be the first endpoint of GB? Will it not be the next point to G? But we cannot find this point if we say that between any points there is another one ever, shall GB have only one end point (i.e. B)? What should we say?
AB is a line (it extends forever in both directions).
AG is a ray (it has a beginning and extends forever in one direction).
What is left (what you are calling GB) is not a line, ray or segment. It might be called an ?open ray? due to it being an open set of points. An open set of points does not include its boundary. A closed set of points does. A line, ray and segment are all closed.