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Math Help - Irrational number proof

  1. #1
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    Irrational number proof

    I'm having trouble understanding how to prove this problem. I need some help.

    Prove that for two arbitrary real numbers a and b, with a < b there is an irrational number c such that a < c < b. Hint(consider a/sqrt(2) and b/sqrt(2))

    Thanks for any help
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by tuyt6444 View Post
    I'm having trouble understanding how to prove this problem. I need some help.

    Prove that for two arbitrary real numbers a and b, with a < b there is an irrational number c such that a < c < b. Hint(consider a/sqrt(2) and b/sqrt(2))

    Thanks for any help
    Hint 2: What inequality can you make with the numbers in the hint?

    Hint 3: Apply the density of \displaystyle \mathbb Q in \displaystyle \mathbb R property and note that \displaystyle r \sqrt 2 is irrational if \displaystyle r \in \mathbb Q...which pretty much is telling you how to solve the problem.
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