A line contains infinitely many points .This is euclid's
Answers
Firstly, that is a beautiful question. Yes, points have no dimensions and yes lines do have length, but it I see untrue that lines are made up of points. Points are not even the part of the line. To understand points let us define points in relation with a line, rather than defining a line in relation with points. Think of this in the following perspective:
A line is a one dimensional figure having no breadth. Points are just assigned to some parts of the line. For e.g.: if we want to measure a part of a line, then to define the extension of this line, we assign a starting point and an ending point. But, when we measure this line, we do not consider the dimensions of the point, that is, we do not consider its size. Hence, points have no dimensions.