There is a one-to-one correspondence between any line and the set of real numbers. This axiom simply says that we can label any line with numbers, much like a ruler.

Elementary Geometry for College Students
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Chapter1: Line And Angle Relationships
Section1.6: Relationships: Perpendicular Lines
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Is there other way of proving this? A proof without the use if bijective functions. Thanks.

There is a one-to-one correspondence between any line and the set of real numbers. This axiom simply says that we can label any line with numbers, much like a ruler.

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