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

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

All lectures in Real Analysis:

Real ANALYSIS -- Modern ANALYSIS -- Advanced CALCULUS