Intervals: Real Numbers

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Real Numbers: Absolute Value and Density

Covers absolute value, density of rationals, and real line topology.

Inequalities on Real Numbers

Explores inequalities on real numbers, including real intervals and comparison properties.

Introduction to Real Numbers and Their Properties

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

Open and Closed Sets MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

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

Real Numbers: Properties and Operations

Covers the properties and operations of real numbers, including divisibility rules and the concept of irreducible fractions.

Decimal Development

Delves into infinite decimal numbers, exploring convergence and divergence, and showcasing examples of rational and irrational numbers.

Boundary Analysis

Explores boundaries in sets, defining them as points not well separated from the set or its complement.

Real Numbers: sqrt(2)MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

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

Real Numbers: Definitions and Properties

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

Intersection: Sets and Properties

Explores the intersection of sets, defining it and discussing its properties.

Square Roots and Irrationality

Explores even squares, irrationality of √2, gaps in rational numbers, and minorants in Q.

Infimum and Supremum of Subsets

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

Functions of Class Ck: Terminology and Definitions MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers the terminology and definitions of functions of class Ck on real number intervals.

Infimum and Supremum: Understanding Bounded Sets

Explains infimum, supremum, Archimedes' properties, rational numbers density, and exercises on irrational numbers and minimum values.

Convex Functions: Theorems and Examples

Discusses the theorems on convex functions and provides examples for better understanding.

Dedekind Cuts: Rational Numbers

Explores Dedekind cuts in rational numbers, essential for constructing real numbers.

Total Order Relation: Properties of Real Numbers

Covers the concept of total order relation and properties of real numbers.

Roots of Real Numbers

Explores the properties and applications of roots of real numbers through practical examples.

Real Numbers: Decimal Notation

Explores the concept of real numbers through decimal notation and fraction representation.

Real Numbers: Order and Completeness Log in to Mediaspace to watch this video

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

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