Matt, I said finite, not fixed. My point is that it is error to refer to a point at infinity in Euclidean space, for a point to exist in Euclidean space, it must be a finite distance from the orgin. The definititon of parallel lines is that every point on one line is a fixed distance from the other line. I was refering to the face that a line can always be positioned so that every point is a fixed distance from another line. This has nothing to do with points at infinity.
1 = .99999... and 89.999... = 90 but there is no point at infinity so what is the problem?