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Lecture
Real Numbers: sqrt(2)
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Related lectures (34)
Introduction to Real Numbers and Their Properties
Introduces real numbers, their properties, and their significance in analysis.
Real Numbers: Definitions and Properties
Explores real numbers, bounds, supremum, infimum, and Archimedean property with practical examples.
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.
Real Numbers: Sets and Operations
Explores the fundamental concepts of real numbers, including sets, operations, and properties like supremum and infimum.
Real Numbers: Sets and Operations
Covers the fundamental concepts related to real numbers, including sets, notations, and operations.
Real Numbers: Sets and Operations
Covers the basics of real numbers and set theory, including subsets, intersections, unions, and set operations.
Infimum and Supremum of Subsets
Covers the concepts of infimum and supremum of subsets in real numbers.
Infimum and Supremum: Understanding Bounded Sets
Explains infimum, supremum, Archimedes' properties, rational numbers density, and exercises on irrational numbers and minimum values.
Real Analysis: Functions and Limits
Covers the basics of real analysis, including functions, limits, and max/min functions.
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 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.
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.
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.
Roots of Real Numbers
Explores the properties and applications of roots of real numbers through practical examples.
Proofs: Contraposition vs. Contradiction
Covers the concepts of contraposition and contradiction in proofs.
Properties of Real Numbers: Bounds, Density, Absolute Value
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Covers the properties of real numbers, including bounds, density, and absolute value.
Real Numbers: Order and Completeness
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Covers the properties of real numbers, focusing on the total order and completeness, including the Archimedean property and the concepts of supremum and infimum.
Introduction to Analysis
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Covers the basics of analysis, including proofs, sets, rational and real numbers, and the concept of infimum.
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