Real Analysis - The Countability of the Rational Numbers

Explore a comprehensive proof demonstrating the countability of rational numbers in this 21-minute video lecture. Delve into an approach that represents the set of rational numbers as a countable union of disjoint finite sets. Follow along as the lecturer constructs the proof, breaking it down into manageable steps and explaining key concepts. Gain insights into the fundamental principles of real analysis and set theory while developing a deeper understanding of the nature of rational numbers and their relationship to countability.

Preliminary result
Proof
Construction
Goal
Proof Part 2