Square Roots and Irrationality

This lecture covers the concept of square roots, focusing on even squares and the irrationality of the square root of 2. It explains the contrapositive method to prove statements about even squares and demonstrates the irrationality of √2 through a proof by contradiction. The presence of 'gaps' in rational numbers is illustrated by the absence of √2 in Q. Examples of minorants in Q are provided, along with the concept of lower bounds. The lecture concludes with the introduction of the set B = {r € Q | r≥ 0, r² ≥ 2}.