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Math Help - irrational between any two rational proof

  1. #1
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    irrational between any two rational proof

    Hey guys new to the forum and have a question of my own,

    I need to prove that for x and y where x<y and both x and y are rational, there exists z where x<z<y and z is irrational.

    the previous part of the question was to find the smallest positive integer n such that ((2)^1/2)/n < .00001

    I think I'm supposed to use this and contradiction to prove one exists as contradiction was used in proofs in the question before

    any help will be greatly apprecitated
    Last edited by 60beetle; March 14th 2008 at 08:24 PM.
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  2. #2
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    Quote Originally Posted by 60beetle View Post
    I need to prove that for x and y where x<y and both x and y are rational, there exists z where x<z<y and z is irrational.
    My suggestion: z = x + (y-x)/\sqrt2.
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  3. #3
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    Quote Originally Posted by Opalg View Post
    My suggestion: z = x + (y-x)/\sqrt2.
    Thanks for that, I knew it would be something relativly simple but it was just one of those days I couldn't get my head around the problem
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