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Math Help - Archimedean property

  1. #1
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    Archimedean property

    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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  2. #2
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    re: Archimedean property

    Quote Originally Posted by facenian View Post
    Does the Archimedean property of real numbers implies the least upper bound axiom? I know it works the other way around
    This can be done. But it may require more than you have to use.
    If you can find Elliot Mendelsonís Number Systems and the Foundations of Analysis then it is in there.
    Mendelson assumes an Archimedean Ordered Field having the Dedekind Cut property.
    Last edited by Plato; July 30th 2011 at 03:28 PM.
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    re: 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.
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