If you have fun with the concept of being able to zoom in to a single Point forever, always getting closer and closer but never arriving, you are one step closer to understanding the concepts of advanced math and calculus.
You saw that with any two points you could always find a point that is exactly in the middle. You can then take this midpoint as a new end point and find another point that is in the middle of it. Since points have no size, you can keep on cutting these line segments in half forever.

No matter how close two points are together, you can still find a point in the middle. Thus, there are an infinite number of points in any line segment, no matter how short it is. This is an example of the concept of a countably infinite set of points. It is possible to write out list the location of these points as their distance from the reference point: 1/2, 1/4, 1/8, 1/16, … and so on forever.

You could just as well cut the segments into thirds, with the location list of points: 1/3, 1/9, 1/27, … and so on forever. Notice that this list of points does not have any of the same points as the one in the last paragraph. So, it appears like you could go on forever filling in all the gaps by dividing the segments up evenly and still never fill in all the gaps. So how many points can fit into the line segment between any two endpoints, no matter how short? Can we ever find a way to fill in all the gaps between points? To fill in all the points between any two points, we would need what is called an uncountably infinite number of points. This is a concept that mathematicians have not yet resolved.