Lectures related to Additional Properties of Real Numbers

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

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

Covers countable and uncountable sets, sequences, summation, and Cantor's Diagonalization proof.

Delves into renormalization, fractals, and strange attractors, exploring the properties of countable and uncountable sets.

Explores countable and uncountable sets, Cantor set, Mandelbrot set, and Box dimension in nonlinear dynamics and complex systems.

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

Explores cardinality, countable sets, and examples of countable and uncountable sets.

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

Introduces measurable sets, functions, and the Cantor set properties, including ternary development of numbers.

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

Covers cardinality of sets, poset, equivalence relations, and geometric progressions through a quiz on Kahoot.

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

Covers the basics of real numbers and set theory, including subsets, intersections, unions, and set operations.

Explores counting infinite sets and decision problems, showcasing the limits of computation in solving certain undecidable problems.

Explores open sets and interior points in real numbers, with examples and criteria for identification.

Covers the fundamental concepts related to real numbers, including sets, notations, and operations.

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

Explores defining arithmetic operations through counting, with insights on cardinal numbers, Cantor's work, and Sudoku.

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

Introduces absolute value, intervals, triangle inequality, and complete numbers in the complex plane.