Properties of Real Numbers

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Related lectures (32)

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.

Real Numbers: Sets and Operations

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

Real Numbers: Definitions and Properties

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

Real Analysis: Functions and Limits

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

Exemple: Infimum and Supremum MOOC: Analysis I MOOC: Analysis I (part 3) : Real number sequences I and II

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

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.

Supremum MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

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

Real Number Sequences: Introduction MOOC: Analysis I MOOC: Analysis I (part 3) : Real number sequences I and II

Introduces real number sequences, limits, and their properties.

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.

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.

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

Introduces the axiomatic structure of real numbers and their properties, including completeness and the Archimedean property.

Boundary Analysis

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

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

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

Dedekind Cuts: Rational Numbers

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

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.

Math-101(en) / Min/Max, Inf/Sup Log in to Mediaspace to watch this video

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

Properties of Real Numbers: Bounds, Density, Absolute Value Log in to Mediaspace to watch this video

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

Interior Points and Closure in Real Analysis Log in to Mediaspace to watch this video

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

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