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Q: Through any two distinct points there are exists exactly one line?

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It takes exactly 2 distinct points to uniquely define a line, i.e. for any two distinct points, there is a unique line containing them.

== == Through any two points there is exactly one straight line.

A CD, because it exists in our dimension, has three distinct points you can measure therefor it is a cylinder.

In plane geometry there is exactly one straight line through two points. There can be any number of curved lines.

one plane LINE

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False!

Collinear points

It takes exactly 2 distinct points to uniquely define a line, i.e. for any two distinct points, there is a unique line containing them.

Unique line assumption. There is exactly one line passing through two distinct points.

Only one line can pass through two distinct points.

No, it is not true. Just think of the three vertices of a triangle.

== == Through any two points there is exactly one straight line.

Infinitely many if the 3 distinct points are collinear. Otherwise just 1.

A CD, because it exists in our dimension, has three distinct points you can measure therefor it is a cylinder.

A CD, because it exists in our dimension, has three distinct points you can measure therefor it is a cylinder.

No, because Of any three points on a line there exists no more than one that lies between the other two.

In plane geometry there is exactly one straight line through two points. There can be any number of curved lines.

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