I was reading about real number system briefly as a part of my pre-calculus study and read about Archimedean property of real numbers which says that
If $ x \gt 0 $ and if * y * is an arbitrary real number, there exists a positive integer * n * such that $ nx \gt y $.
They stated it as a consequence of least upper bound axiom for real numbers. Geometrically they said it means that * any line segment, no matter how long, may be covered by a finite number of line segments of a given positive length, no matter how small. *
I could well understand the statement but could not relate it with the Archimedean property . I thought that may be in this geometric intuition n may mean that finite number of small line segments and x and y be length of the small and large line segments respectively. But I'm not sure about this and need help in this matter. Any suggestions or help is appreciated.
Thanks .