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Lecture
Introduction to Real Numbers
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Related lectures (42)
Real Numbers: Sets and Operations
Covers the fundamental concepts related to real numbers, including sets, notations, and operations.
Real Numbers: Sets and Operations
Explores the fundamental concepts of real numbers, including sets, operations, and properties like supremum and infimum.
Total Order Relation: Properties of Real Numbers
Covers the concept of total order relation and properties of real numbers.
Real Number Sequences: Cauchy Sequences
MOOC: Analysis I
MOOC: Analysis I (part 3) : Real number sequences I and II
Discusses Cauchy sequences, sub-sequences, and numerical series with parameters.
Important Property of Archimedean Bodies
MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers
MOOC: Analysis I
Covers the Archimedean property and the proposition for all x in a set, there exists a positive real number n such that n*x is greater than y.
Real Analysis Basics
Covers the basics of real analysis, including limits, sequences, and continuous functions.
Limits of Sequences
Explores the concept of limits of sequences and their convergence towards infinity or negative infinity.
Convergence in Rº: Definitions and Theorems
Explores convergence in Rº, Cauchy sequences, and the Bolzano-Weierstrass theorem.
Convergence and Limits: Uniqueness and Order
Explores convergence, uniqueness, order, boundedness, and the relationship between boundedness and convergence in sequences.
Infimum and Supremum of Subsets
Covers the concepts of infimum and supremum of subsets in real numbers.
Real Numbers: Sets and Operations
Covers the basics of real numbers and set theory, including subsets, intersections, unions, and set operations.
Real Numbers: Decimal Notation
Explores the concept of real numbers through decimal notation and fraction representation.
Dedekind Cuts: Rational Numbers
Explores Dedekind cuts in rational numbers, essential for constructing real numbers.
Real Numbers: Definitions and Properties
Explores real numbers, bounds, supremum, infimum, and Archimedean property with practical examples.
The Bolzano-Weierstrass Theorem
MOOC: Analysis I
MOOC: Analysis I (part 3) : Real number sequences I and II
Explains the Bolzano-Weierstrass Theorem, stating that every bounded sequence has a convergent subsequence.
Real Numbers Sequences
Explores real number sequences, convergence, limits, boundedness, and monotonicity.
Newton's Binomial and Real Sequences
Explores Newton's binomial theorem and real sequences with examples and definitions.
Introduction to Real Numbers
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Introduces the properties and structure of real numbers, emphasizing completeness and the Archimedean property.
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.
Properties of Real Numbers
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Explains the properties of subsets of real numbers, including Supremum, Infimum, intervals, open sets, and closed sets.
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