Lectures related to Axiom of countability

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

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

Covers the concept of separable L^2 spaces, demonstrating properties and providing examples.

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.

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

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

Covers regular languages, encoding, alphabets, words, languages, concatenation, exponentiation, and iterative closure.

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

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

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

Explores the countability of subsets of real numbers and demonstrates that the set of real numbers is uncountable.

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

Covers the definition and properties of Markov chains, including transition matrix and examples.

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].

Explores countability and undecidable problems in the theory of computation.

Explores equivalence relations, well-ordered sets, geometric series, and countable sets.

Explores toy models, sigma-algebras, T-valued random variables, measures, and independence in probability theory.

Covers the concept of compression and distance boards.