A:wtf wrote: ↑Tue Aug 18, 2020 2:10 amIf you prefer, each point is identical and we associate it with the number that is the location of the point. So there is a point at 2, and a point at pi, and a point at 47, and so forth. You are correct that this is a more precise locution.
To say each point is identical is to say 0=0.
To say 0=0 is to say x=x in that something exists through identity properties.
To say x=x is to say 1=1.
0=1 through x.
To say that a point has a location is to say the point is an entity and as an entity exists as beyond 0 given that zero is nothing. It may be more accurate to say that the point is the position of change from one line (segment) into another line (segment) given the line(s) (segment(s)) are phenomena which are quantifiable given they are forms.
Numbers are the lines not points, unless we equivocate 0 to 1 (which I have no problem with), given the lines are the beginning of form through the projection of nothingness into form. This projection, that of direction, is the beginning of quantifiable forms given that which exists exists through change with this change being the movement of a phenomenon which occurs through direction. One phenomena changes to another, this is movement, and this movement is grounded in direction largely due to the progression from one form into another.