Lectures related to Real Numbers: Structure and Properties

Introduction to Analysis

Covers the basics of analysis, including proofs, sets, rational and real numbers, and the concept of infimum.

Continuity of a Function

Explores the conditions for continuity of a function on real numbers.

Introduction to Real Numbers and Their Properties

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

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.

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.

Intervals: Real Numbers

Explores intervals in real numbers, including open and closed intervals, periodic decimals, and irrational numbers.

Real Numbers: sqrt(2)

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

Real Numbers: Properties and Bounds

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

Real Numbers: Properties and Operations

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

Real Numbers: Absolute Value and Density

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

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

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

Dedekind Cuts: Rational Numbers

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

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.

Intersection: Sets and Properties

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

Introduction to Real Numbers

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

Real Numbers: Sets and Operations

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

Infimum and Supremum: Understanding Bounded Sets

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

Construction of Real Numbers

Discusses the construction and uniqueness of real numbers from rational numbers.