According to the ruler postulate what does the set of points on any line correspond to?

Real numbers.

Explanation:

In a number line, the numbers on the right hand side of zero are all positive numbers (1, 2, 3, 4, ...). On the left hand side of zero are all negative numbers (-1, -2, -3, -4, ...). The numbers in the coordinates of the number line are all real numbers. Thus, the answer is real numbers.