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.
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Two distinct (different) points are needed to determine a line.
a line has to have at least 2 points.a plane has to have at least 3 points.______________It takes two points to define a unique line in Euclidean space. But every line and every line segment contains infinitely many points. The same is true for planes in Euclidean space. You need at least 3 points to define a unique plane, but every plane containes infinitely many points and infinitely many lines or line segments.
A plane can be determined by three points, as long as the three points do not lie along a single line.
A line has an infinite amount of points.