Real Numbers: Axioms and Bounds

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Real Numbers: Order and Completeness Log in to Mediaspace to watch this video

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 Log in to Mediaspace to watch this video

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

Real Numbers: Definitions and Equivalence Classes Log in to Mediaspace to watch this video

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

Construction of Real Numbers Log in to Mediaspace to watch this video

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

More Results on Inf/Sup, Density of Q in R Log in to Mediaspace to watch this video

Covers inf/sup, integral part of real numbers, and density of rational numbers.

Real Numbers: Definitions and Bounds Log in to Mediaspace to watch this video

Explains the definitions and properties of maximum, minimum, supremum, and infimum in real numbers.

Organization, Numbers: Real Numbers and Equations Log in to Mediaspace to watch this video

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

Introduction to Analysis: Understanding Real Numbers and Proofs Log in to Mediaspace to watch this video

Covers the basics of analysis, including real numbers, proofs, sets, and operations.

Real Analysis: Basics and Sequences Log in to Mediaspace to watch this video

Introduces real analysis basics, including functions, sequences, limits, and set properties in R.

Floating Point Representation in Computers Log in to Mediaspace to watch this video

Covers the representation of real numbers in a computer using floating point representation and the dangers of significant digit cancellation.

Extreme Values Theorem Log in to Mediaspace to watch this video

Discusses the Extreme Values Theorem for continuous functions on closed intervals.

Existence of y: Proofs and EDO Resolution Log in to Mediaspace to watch this video

Covers the proof of the existence of y and the resolution of EDOs with practical examples.

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