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Math Help - Archimedian Proof

  1. #1
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    Archimedian Proof

    Suppose x; y in R are rational numbers with x < y. Prove that there exists an irrational
    number z with x < z < y.
    Hint: use the Archimedean property. You may use the fact that square root 2 is irrational, and the fact that a rational plus an irrational is an irrational.

    I'm not sure what he's looking for. I started by using induction, but I got stuck at the induction step as far as how to prove that. I started with a base step of x=0 and y=1, but when i started looking at the problem more, i'm not sure how to account for fractions or things like that.
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  2. #2
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    Re: Archimedian Proof

    Take a look at Theorem 1.3 of http://people.wku.edu/david.neal/337/Reals.pdf. Let me know if you can't follow it.
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