Real Numbers: Axioms and Bounds

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Page 2 of 3

Introduction to Analysis

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

Properties of Real Numbers

Explains the properties of subsets of real numbers, including Supremum, Infimum, intervals, open sets, and closed sets.

Real Numbers: Properties and Bounds

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

Real Analysis: Functions and Limits

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

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.

Quiz on Chapters 1-3: Solutions to TF questions

Covers solutions to true/false questions on subsets, upper bounds, real numbers, and set properties.

Real Numbers: Definitions and Equivalence Classes

Covers the existence of real numbers and equivalence classes of Cauchy sequences.

Construction of Real Numbers

Discusses the construction and uniqueness of real numbers from rational numbers.

Real Numbers: sqrt(2)

Explores real numbers, focusing on the square root of 2 and the implications of its irrationality.

Exemple: Infimum and Supremum

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