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If x and y are arbitrary real numbers such that x < y, prove that...

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Advance Math

If x and y are arbitrary real numbers such that x < y, prove that there exists at least one rational number r satisfying x < r < y, and hence infinitely many.

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Since y x 0 by the Archimedean property there exists a positive integer n such that ny x 1 Now let m nx the greatest integer    See Answer
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