Liouville's Number, the Easiest Transcendental and Its Clones

Liouville's Number, the Easiest Transcendental and Its Clones

Explore the fascinating world of transcendental numbers in this 21-minute video lecture focusing on Liouville's number. Delve into a unique and accessible proof of its transcendence, not found in typical textbooks. Discover how to create a paradoxical clone of real numbers using Liouville's number as a template, resulting in an uncountably infinite set of measure zero. Learn about the historical context, including Liouville's original paper, and gain insights into the mathematical concepts of transcendental numbers, proof by contradiction, and measure theory. Engage with cool facts and a comprehensive exploration of this intriguing mathematical topic, complete with visual aids and expert explanations.