Lectures related to Organization, Numbers: Real Numbers and Equations

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

Covers the organization of real numbers, axioms, and bounds, including infimum and supremum.

Covers countability and bijections between sets, demonstrating the uncountability of real numbers.

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

Covers the properties of real numbers, including bounds, density, and absolute value.

Introduces real numbers, their properties, and their significance in analysis.

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

Covers the concept of total order relation and properties of real numbers.

Explores Dedekind cuts in rational numbers, essential for constructing real numbers.

Explains Cantor's theorem comparing cardinalities of different number sets.

Covers the concept of area, axioms, and the area of rectangles.

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

Covers the structure and properties of real numbers, including the introduction to the axiomatic system and the implications of Archimedean property.

Covers minimum, maximum, infimum, and supremum concepts in real numbers with examples and proofs.

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

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

Explores the conditions for continuity of a function on real numbers.

Explores real numbers, including supremum, infimum, maximum, and minimum properties.

Covers the basics of linear algebra and systems of equations with exercises and IT tools for support.

Explores the proposition that X² is not equal to 2 using absurd reasoning.