How many points in a line segment? My teacher said that in the circumference of circle there are infinite points. When I was learning more about circle, I came to this picture:



My question is: When we unroll the circle, then the length of the circle and line segment are the same. For this reason, I think that the unrolled line segment should also have infinite points! But there are only two end points. Can anyone explain to me where am I going wrong?
You are conflating end points and points.


The circumference of a circle does not have any end points but infinitely many points.
The line segment has two end points and still infinitely many points.


Sidenote: The length of the segment is not as important as you may think. We cannot distinguish the number of points on a line segment of length $π$ from those on a line segment of length $2π$.
Any legitimate question depends on whether the terminology is understood correctly. The problem is, the definition of a "point" is not understood correctly. Your teacher believes a point has no size because most, if not all, of the geometry books, old and new, say so. It is an error of immense proportions, wasting people's time and even warping their thinking. Geometry is supposed to help us understand the physical world around us. If a point has no size, then it has zero size. Basic math tells us that no matter how many times you add zero, it will always equal zero. 

The correct definition of a POINT is "the smallest possible size". From there, everything will make sense mathematically, and logically. Both a circle, and a line segment, have an "indefinite" amount of points, but surely finite.