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Math Help - help on irrational numbers

  1. #1
    Junior Member
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    help on irrational numbers

    suppose x is an irrational number
    -show that 1/x is irrational
    -are there any integers p/q both greater than 0 such that (p/q)x is rational?

    suppose x is an irrational number and y is any real number bigger than zero. show that at least one of x-y and x+y is an irrational number. .

    thank you
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  2. #2
    MHF Contributor red_dog's Avatar
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    Suppose that \frac{1}{x} is rational.

    Then \frac{1}{x}=\frac{p}{q}\Rightarrow x=\frac{q}{p}\Rightarrow x is rational, contradiction

    Suppose \frac{p}{q}\cdot x=\frac{m}{n}\Rightarrow x=\frac{mq}{np}, contradiction.
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