Concept

Cantor's theorem

Related lectures (12)

Explores the construction of the Lebesgue function on the Cantor set and its unique properties.

Fractal Uncertainty Principle and Spectral Gaps

Explores transfer operators, Patterson-Sullivan measure, FUP, spectral gaps, and resonances in Schottky groups.

Computing leading eigenvalues of the transfer operator

Explores computing the leading eigenvalue of a transfer operator beyond periodic points, focusing on mathematical settings, spectral radius estimation, and the Zaremba Conjecture.

Analysis IV: Measurable Sets and Functions

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

Relations, Sequences and Summations

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

Hausdorff Dimension and Brownian Motion

Explores the Hausdorff dimension of Brownian motion zeros, demonstrating a dimension of 1/2 with certainty.

Different Infinities: Cantor's Theorem

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

Change of Variable Formula: Devil's Staircase

Explores a change of variable formula and the intriguing Devil's Staircase.

Relations, Sequences, Summation: Cantor Diagonalization

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

Nonlinear Dynamics: Chaos and Complex Systems

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

Cantor-Heine Theorem

Covers the Cantor-Heine theorem, discussing uniform continuity and compactness.

Selected Topics in Mathematics

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