Dedekind Cuts: Rational Numbers

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Real Analysis: Functions and Limits

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

Real Number Sequences: Introduction

Introduces real number sequences, limits, and their properties.

Complex Numbers: Algebraic Structures and Applications

Covers algebraic structures, real numbers, fields, and the applications of complex numbers in science and engineering.

Interior Points and Closure in Real Analysis

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

Q is a Field

Covers the properties of rational numbers and introduces the concept of an ordered field in Q.

Organization, Numbers: Real Numbers and Equations

Introduces real numbers, including equations like x²=2 with no rational solutions.

Construction of Real Numbers

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

Intersection: Sets and Properties

Explores the intersection of sets, defining it and discussing its properties.

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.

Real Numbers: Definitions and Properties

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