[Math] How many points in a line segment

elementary-set-theoryinfinity

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:

cirle

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?

Best Answer

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 $2π$.

Related Question