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Math Help - Inverse of irrational number

  1. #1
    Newbie
    Joined
    Apr 2009
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    4

    Inverse of irrational number

    Hi,

    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
    Joined
    Mar 2007
    Posts
    1,240

    Talking

    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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