Topics in analysis

Related lectures (31)

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

Covers selected topics in mathematics, including Taylor approximations and algebraic structures of Z and K[X].

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

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

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

Covers the concepts of infimum and supremum of subsets in real numbers.

Explores the fundamental concepts of real numbers, including sets, operations, and properties like supremum and infimum.

Delves into infinite decimal numbers, exploring convergence and divergence, and showcasing examples of rational and irrational numbers.

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

Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

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

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

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

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Explores countable and uncountable sets, demonstrating how to determine the cardinality of different sets through listing elements in a sequence.

Introduces real number sequences, limits, and their properties.

Explains infimum, supremum, Archimedes' properties, rational numbers density, and exercises on irrational numbers and minimum values.

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

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

Covers strings, countable sets, cardinality, and the concept of countability, exploring the countability of various sets and Cantor diagonalization.

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