1. 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.

2. Originally Posted by friday616
Prove that square root(n-1) + square root(n+1) is irrational for every positive integer n.
Hint: if $\displaystyle x^2$ is irrational then so is $\displaystyle x$. So look at $\displaystyle \bigl(\sqrt{n-1}+\sqrt{n+1}\bigr)^2$.