Discrete Mathematical Structures, Lecture 3.2: Parity, and proving existential statements

Discrete Mathematical Structures, Lecture 3.2: Parity, and proving existential statements.

In this lecture, we prove a few basic results about numbers that involve existential statements. For example, an integer n is even if there exists an integer k such that n=2k, and is odd if there exists an integer k such that n=2k+1. Proof methods in this lecture fall into three categories: constructive, non-constructive, and indirect (contrapositive or contradiction).

[chaoshengzhe]

It seems that √2^√2 is indeed irrational by Gelfond–Schneider theorem.