The ruler postulate states that:
- Every point on a line can be paired with a real number.
- The number associated with a point A on the line is called the coordinate of A.
- Two arbitrary points can be paired with the numbers 0 and 1, defining the length of a unit.
- The distance between any two points <var>A</var> and <var>B</var> is designated AB.
- The distance between two points A and B can be found by taking the absolute value of the difference of their coordinates: AB = |A - B|. Note that this implies that a distance is always positive.