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Math Help - Irrational Numbers q+a

  1. #1
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    Irrational Numbers q+a

    Let q belong to Q, and a belong to R\Q. Prove

    q+a is irrational

    so you let q = m/n

    Not sure how to go about solving this, thanks
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  2. #2
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    Quote Originally Posted by glover_m View Post
    Let q belong to Q, and a belong to R\Q. Prove

    q+a is irrational

    so you let q = m/n

    Not sure how to go about solving this, thanks
    You can use contradiction :

    suppose q +a is rational ====> q+a=x/y where x,y are integers ,but also q is rational so q=z/w ,where again z,w are integers ,hence:


    ..............a= x/y -z/w a rational ,thus contradiction
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