Concept

Cartesian product

Related lectures (30)

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Cartesian Product in Linear Algebra

Explores the Cartesian product in linear algebra and the method of induction for proving propositions.

Cartesian Product: Sets and Recurrence

Explores the Cartesian product of sets, subsets, and recurrence in mathematics with examples and exercises.

Cartesian Product

Covers the concept of the Cartesian product, emphasizing the order of elements in pairs.

Counting: The Product Rule

Explores the Product Rule for counting tasks and sets.

Sets and Relations

Introduces sets, Cartesian product, order importance, and relations on sets.

Cartesian Product and Equivalence Classes

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

Commutation Groups: Euler's Totient Function

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

Sets, Functions and Relations: Q&A

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

Properties of Cartesian Products and Disjoint Unions

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

Binary Relations and Cartesian Products

Explores binary relations, Cartesian products, and applications between sets, emphasizing their properties and significance.

Counting Basics: Set Theory and Permutations

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

Arc Length Approximation

Explores arc length calculation for curves and polygons inscribed in circles using trigonometry and parametric equations.

Properties of Operations: Equivalence Relations and Logic Basics

Explores properties of operations, equivalence relations, and logic basics.

Introduction to Categories: Products and Coproducts

Introduces the theory of categories by generalizing the Cartesian product and disjoint union of sets to any category.

Sets and Functions

Introduces sets, functions, and proofs in mathematics, covering set equality, subsets, Cartesian products, and truth sets of predicates.

Set Identities: Analogues and Proofs

Explores set identities as analogues of logical equivalences in propositional logic.

Advanced Physics I

Covers advanced topics in physics, focusing on demonstrations and directions related to proportional motion, circular movement, and coordinate systems.

Mathematics: Sets and Functions

Introduces sets, functions, Cartesian products, and compositions, discussing images, preimages, and function properties.

Group Actions on Sets

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