prove that:
√3 = inf{ x in rationals: x > 0 and x^2 > 3}
thank you for your time!
Let $\displaystyle A=\inf\{x\in \mathbb{Q}:0<x\land x^2>3\}$ and suposse $\displaystyle A\neq \sqrt{3}$. Then $\displaystyle A>3$ or $\displaystyle A<3$.
Now you can use the fact that $\displaystyle \mathbb{Q}\subset \mathbb{R}\subset \overline{\mathbb{Q}}$.