Philosophy of A Number Line

It is said that individual points on a number line, are without dimension. If this is so, then how is it, that the total collection of points has dimension. It is linear, which demands dimension. Where, and how, did all of these little points without dimension, suddenly posses dimension as a collective. Setting this aside...

If I take my finger, or pencil and place it on a "point". I then move it left, or right to another point. I must traverse, or move through, other points. Yet these points I move through, have no dimension. One cannot move through that which has no dimension. Space is required to move. Therefore, these points on a number line, cannot be absent dimension.

Points on a number line, have dimension. It is only that their dimension is infinitesimally small, and cannot be measured from out perspective.

Further, this then shows, that zero has, or is dimension. (-1+1=0) and not 1. I move one space, or dimension to the right. Which is zero.