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Math Help - Prove by Archimedian property

  1. #1
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    Prove by Archimedian property

    Here is the problem:

    Use the Archimedian property to prove that if a,b belongs to R (real number) with 0< a < b, then there is a rational number p/q with p and q both odd such that a<p/q<b. (Remark: Modify the proof that rationals are dense.)

    Here is my work:

    By the Archimedian property, there exists an odd q belongs to R such that 1 < qa implies that 1/q < a. By the Archimedian property agian, there exists an odd p belongs to R such that a<p/q<b.

    Is it right???
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  2. #2
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    Can you show that if c-d>1 then there is an integer such that d<J<c~?
    If so we know there us an integer such that 1<Kb-Ka. So \dfrac{J}{K} is between them.
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  3. #3
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    Thank you ~ problem solved
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