Tag: number-theory

Constructive Criticism

Here is a classical example of a non-constructive proof. Thm 1. There exist irrational numbers \(x,y\) such that \(x^y\) is rational. Proof. If \(\sqrt{2}^{\sqrt{2}}\) is rational, then we may take \(x=y=\sqrt{2}\). Otherwise, we may tak…