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Math Help - Real Analysis

  1. #1
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    Real Analysis

    I have a few analysis questions. Any help is much appreciated, thanks!

    1. Prove that square root(n-1) + square root(n+1) is irrational for every positive integer n.

    2. Prove that the set (x element in R: 10squareroot(x)-x greater than 0) is bounded.

    3. Prove that every finite set is bounded.

    4. Prove that the infimum and the supremum of the interval (a, b) are a and b, respectively.
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  2. #2
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    Quote Originally Posted by friday616 View Post
    Prove that square root(n-1) + square root(n+1) is irrational for every positive integer n.
    Hint: if x^2 is irrational then so is x. So look at \bigl(\sqrt{n-1}+\sqrt{n+1}\bigr)^2.
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