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Thread: Inverse of irrational number

  1. #1
    Apr 2009

    Inverse of irrational number


    How do I prove that the inverse of an irrational number is irrational? I'm stumped.

    Thanks for any help with this.
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  2. #2
    MHF Contributor
    Mar 2007


    By "inverse", do you mean "reciprocal"? If so, then you might proceed by contradiction:

    Assume that x is irrational, with reciprocal 1/x = y. Suppose y is rational, so y = p/q for some integers p and q. Then 1/y = q/p = x, so...

    How does that end?
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