Ruler postulate
The points on a line can be put into a one-to-one correspondence with the real numbers.
The ruler postulate is a basic postulate in Euclidean geometry that states that any two points on a line can be matched with real numbers so that, given two points, the coordinates of any point between the two can be found by taking the average of the coordinates of the two given points. This postulate establishes the concept of a ruler as a tool for measuring distances along a line. It also implies that the distance between any two points can be calculated by taking the absolute value of the difference between their coordinates. The ruler postulate is a fundamental concept in geometry and is used to establish many other important theorems and postulates.
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