> Lines are not ?made up? of points. When you say ?made > up? you imply stacked or connected, one after the > other. But as has been established here, even by some > of your own posts, points cannot be stacked or > connected. Thus, lines cannot be "made up" of points. > > Lines can be said to be ?made up? of smaller lines. > > Most (probably all) of the issues you are having in > understanding the answers you are being given, and > that you requested, is that you have a poorly > conceived notion of ?point?. Points are > dimensionless. That doesn?t mean they have zero > length. That means they don?t even have the notion of > length.
Therefore, a line is that which has only length, and each line can be considered made up of smaller lines and these of smaller and so on, and we imagine the extremities of a line as points, and if we want to cut a straight-line into two ones, we consider a point between the two endpoints (i.e. one point on the straight-line), which has no length and no width, is dimensionless, and therefore it doesn't fill any space on the straight-line but cuts the line into two lines which can be disjoint without any trouble. And when two lines (which are not parallel) meet each other, they simply cut their length into two ones, like a point, and therefore we say that two lines meet one another in a point. So, the point is only something that we imagine on a line that helps us to divide the length of the line, and so as to name the extremities of line we imagine them as points, and therefore points (being dimensionless) do not actually interfere in the process of division of a line! I'm impressed, I'm going to contemplate the meaning of what has been said, but I think this to be satisfactory for our purpose unless other doubts will arise