Explore the mathematical contributions and skepticism of Emile Borel in this 24-minute video lecture from the Sociology and Pure Mathematics series. Delve into Borel's concept of normal numbers and his intriguing "know-it-all number" while examining the foundations of real number theory. Gain insights into the intersection of pure mathematics and critical social analysis as you investigate infinite decimals, base 10 normal numbers, and Borel's unique perspective on the nature of real numbers. Prepare for a thought-provoking discussion that challenges conventional understanding of mathematical concepts and sets the stage for further exploration of Borel's work, including his French publication "Les Nombres Inaccessibles."