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Math Help - Archimedean property

  1. #1
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    Lightbulb Archimedean property

    Hello,

    I'm preparing for a competitive exam which would include questions on the following topics.

    i) Real number system as a complete ordered field
    ii) Archimedean property


    Can you please refer some website where I can get questions on these topics?

    thanks in advance,
    MAX
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  2. #2
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    Quote Originally Posted by MAX09 View Post
    Hello,

    I'm preparing for a competitive exam which would include questions on the following topics.

    i) Real number system as a complete ordered field
    ii) Archimedean property


    Can you please refer some website where I can get questions on these topics?

    thanks in advance,
    MAX

    What about books instead of sites? try Lang's "Algebra", or Dummit and Foote's "Abstract Algebra".

    Tonio
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  3. #3
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by MAX09 View Post
    Hello,

    I'm preparing for a competitive exam which would include questions on the following topics.

    i) Real number system as a complete ordered field
    ii) Archimedean property


    Can you please refer some website where I can get questions on these topics?

    thanks in advance,
    MAX
    Here are two questions:

    1) If x\in\mathbb{R} and x>0, prove that there exists a unique m\in\mathbb{N} such that m-1\leq x< m.

    2) Prove that there exists a rational number between any two real numbers x and y.
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