Concept

Monotonic function

Related lectures (32)

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

Covers the squeeze theorem, monotone sequences, subsequences, and Bolzano-Weierstrass theorem, emphasizing the importance of peaks in sequences.

Explores continuous strictly monotone functions, differentiability, and linear function approximation.

Covers continuity, differentiation, and algebraic operations, including the computation of derivatives for various functions.

Focuses on injective functions in linear algebra, demonstrating how to verify properties and prove injectivity.

Covers the properties of real functions, domains, and types of functions, including periodicity.

Covers the Prokhorov Theorem in Optimal Transport, emphasizing support sets and optimality conditions.

Discusses the Dini theorem for the uniform convergence of monotonically increasing or decreasing functions.

Explores the convergence and limit of geometric series, demonstrating mathematical properties and applications.

Covers Taylor's approximation theorem, differentiability, error control, and function expansions.

Covers the basic properties of real number sequences, including definitions for increasing and decreasing sequences.

Explores various number sequences, limits, and properties of arithmetic, geometric, and harmonic sequences.