The Archimedean Property | Real Analysis | Lecture 5

Proof of the Archimedean Property of the natural and real numbers. Proof that the set of natural numbers is not bounded from above. Proof of the existence of a maximal element in a bounded subset of the integers. 00:00 Introduction 00:31 If a set A \subset Z has a supremum, then sup A belongs to A. Proof. 08:45 The Archimedean Property with proof. 16:56 Example. The set of natural numbers is not bounded from above. Related lectures: Lecture 4 | Real Analysis | Epsilon Criterion for Supremum and Infimum | Examples of Sup and Inf    • The Epsilon Criterion for Supremum and Inf...   Lecture 3 | Real Analysis | Axioms of Real Numbers | Part 3: The Completeness Axiom | Sup and Inf    • Axioms of Real Numbers | Part 3: The Compl...   All lectures in Real Analysis: Real ANALYSIS -- Modern ANALYSIS -- Advanced CALCULUS    • Real ANALYSIS -- Modern ANALYSIS -- Advanc...