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Math Help - Between a rational and a irrational

  1. #1
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    Between a rational and a irrational

    Hello.
    Between a rational and a irrational is there a rational? and a irrational? and vice-versa?
    I know that between 2 rationals there is a rational and a irrational and that between 2 irrationals there is a rational and a irrational, but i cannot figure this out... please help.
    Thanks.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by nerdy_time View Post
    Hello.
    Between a rational and a irrational is there a rational? and a irrational? and vice-versa?
    I know that between 2 rationals there is a rational and a irrational and that between 2 irrationals there is a rational and a irrational, but i cannot figure this out... please help.
    Thanks.
    If I remember this proof is best done assuming that it is false and finding a contradiction. Why don't you try it and report back.
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  3. #3
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    Quote Originally Posted by Mathstud28 View Post
    If I remember this proof is best done assuming that it is false and finding a contradiction. Why don't you try it and report back.
    So...it is true? Right? I am not worried about the proof for now.
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  4. #4
    Moo
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    Hello,
    Quote Originally Posted by nerdy_time View Post
    So...it is true? Right? I am not worried about the proof for now.
    Yes it is true, though the most common proof is about "there is a rational between two irrationals" or "there is an irrational between two rationals"
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