The axiom of the arrangement of points on the line

Of the three points located on one straight line, one and only one lies between the two others.

This statement is an axiom, that is, it is initially accepted as true and can not be proved.

Comments

Three points are given: A, B, C.

Possible variants of the arrangement of three points on a straight line are shown in Fig.



Points lying on one straight line. Of the three points located on one straight line, one and only one lies between the two others.

In the first variant, B lies between A and C on the straight line a; in the second variant, A lies between C and B on the straight line a; in the third variant, C lies between B and A on the straight line a. Other options can not be.