How many points are in a unique line?

Answer 1

Every line and every line segment of >0 length has an inifinite amount of unique points.

Socratic Explaination:

consider ...
- There are 2 distinct points defining a line segment.
- Between these 2 distinct points, there is a midpoint.
- The midpoint divides the original segment into 2 segments of equal length.
- There are 2 distinct points used to define each segment.
- Between these 2 distinct points, there is a midpoint for each segment.
- These midpoints divide the segments into smaller segments of equal length.
- repeat until throughly beaten

This leads to a description of an infinite amount of points for any given line segment.

This does not describe all the points of a line segment. Example: the points 1/3 of the distance from either of the the original 2 points are approached but never hit.

Please, feel free to rephrase this explanation. I know it's sloppy.