Lectures related to Properties of Real Numbers

Real Numbers: Order and Completeness

Covers the properties of real numbers, focusing on the total order and completeness, including the Archimedean property and the concepts of supremum and infimum.

Real Numbers: Sets and Operations

Explores the fundamental concepts of real numbers, including sets, operations, and properties like supremum and infimum.

Infimum and Supremum of Subsets

Covers the concepts of infimum and supremum of subsets in real numbers.

Math-101(en) / Min/Max, Inf/Sup

Covers minimum, maximum, infimum, and supremum concepts in real numbers with examples and proofs.

Real Numbers: Sets and Operations

Covers the fundamental concepts related to real numbers, including sets, notations, and operations.

Properties of Real Numbers: Bounds, Density, Absolute Value

Covers the properties of real numbers, including bounds, density, and absolute value.

Real Numbers: Definitions and Properties

Explores real numbers, bounds, supremum, infimum, and Archimedean property with practical examples.

Interior Points and Closure in Real Analysis

Explores interior points, closures, and set properties in real analysis.

Real Analysis: Functions and Limits

Covers the basics of real analysis, including functions, limits, and max/min functions.

Quiz on Chapters 1-3: Solutions to TF questions

Covers solutions to true/false questions on subsets, upper bounds, real numbers, and set properties.

Exemple: Infimum and Supremum

Illustrates the calculation of infimum and supremum for a set of elements.

Real Numbers: Properties and Formulas

Explores real numbers, including supremum, infimum, maximum, and minimum properties.

Introduction to Real Numbers

Introduces the properties and structure of real numbers, emphasizing completeness and the Archimedean property.

Open and Closed Sets

Explains the concepts of open and closed sets in real numbers.

Real Numbers: Axioms and Bounds

Covers the organization of real numbers, axioms, and bounds, including infimum and supremum.

Real Numbers: Definitions and Bounds

Explains the definitions and properties of maximum, minimum, supremum, and infimum in real numbers.

Real Numbers: Definitions and Equivalence Classes

Covers the existence of real numbers and equivalence classes of Cauchy sequences.

Real Analysis: Basics and Sequences

Introduces real analysis basics, including functions, sequences, limits, and set properties in R.

More Results on Inf/Sup, Density of Q in R

Covers inf/sup, integral part of real numbers, and density of rational numbers.

Supremum

Covers the concept of supremum in real numbers and its properties as the least upper bound of a set.