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Lecture
Properties of Real Numbers: Bounds, Density, Absolute Value
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Related lectures (38)
Introduction to Real Numbers and Their Properties
Introduces real numbers, their properties, and their significance in analysis.
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.
Infimum and Supremum of Subsets
Covers the concepts of infimum and supremum of subsets in real numbers.
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 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 Analysis: Functions and Limits
Covers the basics of real analysis, including functions, limits, and max/min functions.
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.
Proofs: Contraposition vs. Contradiction
Covers the concepts of contraposition and contradiction in proofs.
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.
Elementary Algebra: Numeric Sets
Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.
Real Numbers: Absolute Value and Density
Covers absolute value, density of rationals, and real line topology.
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.
Infimum
MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers
MOOC: Analysis I
Explains the concept of infimum in real numbers and its properties.
Introduction to Analysis
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Covers the basics of analysis, including proofs, sets, rational and real numbers, and the concept of infimum.
Math-101(en) / Min/Max, Inf/Sup
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Covers minimum, maximum, infimum, and supremum concepts in real numbers with examples and proofs.
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.
Real Numbers: Axioms and Bounds
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Covers the organization of real numbers, axioms, and bounds, including infimum and supremum.
Real Numbers: Properties and Bounds
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Explores real numbers' properties, bounds, limits, and density in the number line.
Real Numbers: Properties and Formulas
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Explores real numbers, including supremum, infimum, maximum, and minimum properties.
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