Does the Archimedean property of real numbers implies the least upper bound axiom? I know it works the other way around

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- Jul 30th 2011, 02:02 PMfacenianArchimedean property
Does the Archimedean property of real numbers implies the least upper bound axiom? I know it works the other way around

- Jul 30th 2011, 03:08 PMPlatore: Archimedean property
- Jul 31st 2011, 01:38 AMHallsofIvyre: Archimedean property
The Archimedian property of the real numbers is simply that, given any real number, there exist an integer larger than that given number. No, you cannot prove the least upper bound property from that, alone, because the Archimedian property also holds for the set of rational numbers but the least upper bound property does not.