Real Numbers: sqrt(2)

This lecture covers the concept of real numbers, specifically focusing on the square root of 2. It discusses the properties of the set A = {x ∈ R: x > 0, x² < 2}, explores the supremum of A, and analyzes the implications of different scenarios where a² is compared to 2. Through a series of mathematical derivations, it demonstrates contradictions and concludes with the proof that √2 is an irrational number.