I didn't say that AB is an endless line in both directions, I said that AB is a finite straight-line (having the endpoints A and B), therefore AG and GB in which AB has been divided are also finite straight-lines. About the "open ray": how can a finite straight-line have no boundary???? Being made of points, there must be two boundaries in both directions, which we call endpoints, for if there is no boundary this is not a finite straight-line but an infinite one. Therefore I don't understand your notion of "open ray", but if you are willing to explain me this concept in detail and make me understand, I will be grateful.
> > 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. > > http://en.wikipedia.org/wiki/Boundary_(topology) > > Bob Hansen