Lectures related to Real Numbers: Definitions and Bounds

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

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

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

Properties of Real Numbers: Bounds, Density, Absolute Value

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

Properties of Real Numbers

Explains the properties of subsets of real numbers, including Supremum, Infimum, intervals, open sets, and closed sets.

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.

Infimum and Supremum of Subsets

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

Real Numbers: Properties and Formulas

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

Quiz on Chapters 1-3: Solutions to TF questions

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

Supremum

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

Real Analysis: Functions and Limits

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

Introduction to Real Numbers and Their Properties

Introduces real numbers, their properties, and their significance in analysis.

Real Numbers: Properties and Bounds

Explores real numbers' properties, bounds, limits, and density in the number line.

Real Numbers: Definitions and Equivalence Classes

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

Real Numbers: Axioms and Bounds

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

Real Numbers: Definitions and Properties

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

Exemple: Infimum and Supremum

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

Real Number Sequences: Introduction

Introduces real number sequences, limits, and their properties.

Infimum

Explains the concept of infimum in real numbers and its properties.

Real Numbers: sqrt(2)

Explores real numbers, focusing on the square root of 2 and the implications of its irrationality.