Notes
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1. Given any two points A and B, there is exactly one line AB
passing through them.
2. The Distance Postulate: For any two distinct points, there exists
a unique positive number called the distance between the two
points.
3. The Ruler Postulate: The set of points on any line are in one-to-
one correspondence with the set of real numbers such that the
distance between a pair of points is identified as the absolute
value of the difference of the corresponding real numbers.
4. The Ruler Placement Postulate: Given any two points A and B on
a line, a coordinate system can be chosen in such a way that the
coordinate of A is zero and the coordinate of B is positive. This
axiom ensures that any point can be chosen as the origin. That
point, together with any other point, can be used to define a
positive distance.
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