Lectures related to Continuity of a Function

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

Properties of Real Numbers: Bounds, Density, Absolute Value

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

Introduction to Real Numbers and Their Properties

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

Covers the structure and properties of real numbers, including the introduction to the axiomatic system and the implications of Archimedean property.

Intervals: Real Numbers

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

Real Numbers: Properties and Bounds

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

Real Numbers: sqrt(2)

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.

Real Numbers: Absolute Value and Density

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

Real Numbers: Properties and Operations

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

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.

Square Roots and Irrationality

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

Intersection: Sets and Properties

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

Dedekind Cuts: Rational Numbers

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

Roots of Real Numbers

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

Infimum and Supremum: Understanding Bounded Sets

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

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

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

Real Analysis: Basics and Sequences

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

Real Numbers: Properties and Formulas

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

Real Numbers: Sets and Operations

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