Equivalence Relations and Functions

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Related lectures (28)

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Definitions and Notations

Covers the definitions and notations related to functions.

Cartesian Products and Equivalence Relations

Introduces Cartesian products, equivalence relations, and functions, emphasizing the importance of order and discussing injective, surjective, and bijective functions.

Functions: properties and convergence criteria

Explores convergence criteria, function properties, and unique element association.

Function Properties: Injective, Surjective, Bijective

Explains injective, surjective, and bijective functions using examples and graphs.

Equivalence Classes and Relations

Covers equivalence classes, relations, quotient sets, and functions properties.

Mathematical Analysis: Functions and Composition

Covers the analysis of functions, composition, and mathematical induction.

Operations on Sets: Parts, Intersection, and Difference

Explores operations on sets, Cartesian products, and functions' properties.

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Sets, Functions and Relations: Q&A

Covers examples of relation composition, Cartesian product, and injective functions.

Sets and Functions

Introduces sets, functions, and their properties, including injective and surjective functions, composition, and inverse functions.