Lectures related to Different Infinities: Cantor's Theorem

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

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

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

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

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

Explores intervals in real numbers, including open and closed intervals, periodic decimals, and irrational numbers.

Explores boundaries in sets, defining them as points not well separated from the set or its complement.