Axioms of Real Numbers | Part 3: The Completeness Axiom | Sup and Inf | Real Analysis | Lecture 3

This lecture on Real Analysis covers the completeness axiom of real numbers. The definitions of bounded sets, supremum, and infimum are discussed. It is shown that the square root of 2 is not a rational number and that it is a real number. 00:00 Introduction 1:38 Proof of the fact that sqrt(2) is not rational 8:49 Definition of a set bounded from above/below, definitions of supremum and infimum 16:53 The completeness axiom of real numbers 22:31 Example 28:12 Proof of the fact that sqrt(2) is a real number Related lectures: Axioms of Real Numbers | Part 1: Field Axioms | Real Analysis | Lecture 1 https://youtu.be/8rhYgJSWYdA Axioms of Real Numbers | Part 2: Ordered Field Axioms | Real Analysis | Lecture 2 https://youtu.be/WjMdBKNPaGU All lectures in Real Analysis: Real ANALYSIS -- Modern ANALYSIS -- Advanced CALCULUS https://www.youtube.com/playlist?list=PLo2_-dFVnlxyKp_xgJ9Jsuj4Vuy09Row6