Counting: The Product Rule

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Cartesian Products and Equivalence Relations

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

Sets, Functions and Relations: Q&A

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

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Functions: Definitions and Notations

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Cartesian Product and Equivalence Classes

Covers the Cartesian product of sets and binary relations with detailed examples and graphical representations.

Sets and Operations: Introduction to Mathematics

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Properties of Cartesian Products and Disjoint Unions

Introduces essential properties of Cartesian products and disjoint unions in the theory of groups and categories.

Commutation Groups: Euler's Totient Function

Explores commutative groups, Euler's Totient Function, and Cartesian products in group theory.

Group Actions on Sets

Explores group actions on sets through homomorphisms and Cartesian products, illustrating their properties and equivalent definitions.

Counting Basics: Set Theory and Permutations

Covers the main rules of counting for combinatorial objects and introduces various counting techniques.