In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is in A and b is in B. In terms of set-builder notation, that is A table can be created by taking the Cartesian product of a set of rows and a set of columns. If the Cartesian product rows × columns is taken, the cells of the table contain ordered pairs of the form (row value, column value). One can similarly define the Cartesian product of n sets, also known as an n-fold Cartesian product, which can be represented by an n-dimensional array, where each element is an n-tuple. An ordered pair is a 2-tuple or couple. More generally still, one can define the Cartesian product of an indexed family of sets. The Cartesian product is named after René Descartes, whose formulation of analytic geometry gave rise to the concept, which is further generalized in terms of direct product. (Wikipedia).
The Basics of Sets | Cartesian Products
We define the Cartesian product of sets and work through several examples. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal Website: http://www.michael-penn.net Randolph College Math: http://www.randolphcollege.edu/mathematics/ Research Gate profile:
From playlist Proof Writing
What is the Cartesian Product of Sets? | Set Theory
What is the Cartesian product of two sets? The Cartesian product can be generalized to more than two sets, but in this video we go over Cartesian products of two sets! Here is how it works. If you have two sets, A and B, then their Cartesian product, written A x B, is the set containing al
From playlist Set Theory
Cartesian Products with Empty Sets | Set Theory, Cartesian Product of Sets, Empty Set
How do Cartesian products work with empty sets? Cartesian products are great and all, but we cannot eagerly dive into working with them without making sure we know how to deal with Cartesian products when empty sets are involved. We go over that in today's math lesson! Recall that the Car
From playlist Set Theory
The vector cross-product is another form of vector multiplication and results in another vector. In this tutorial I show you a simple way of calculating the cross product of two vectors.
From playlist Introducing linear algebra
Cartesian Product of Two Sets A x B
Learning Objectives: 1) Define an ordered pair 2) Define the Cartesian Product of two sets 3) Find all the elements in a Cartesian Product **************************************************** YOUR TURN! Learning math requires more than just watching videos, so make sure you reflect, ask q
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
The Cartesian Product of Two Sets
This video explains how to find the Cartesian product of two sets.
From playlist Sets (Discrete Math)
How to make Cartesian Diver! Materials : Two coins, plastic straw, gas lighter, tacks, soda bottle
From playlist MECHANICS
Topology 1.4 : Product Topology Introduction
In this video, I define the product topology, and introduce the general cartesian product. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Topology
Calculus 3: Vector Calculus in 3-D (18 of 35) What is a Cross Product?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a cross product. The cross product of 2 vectors A and B is another vector C and is directed perpendicular to the plane containing A and B. Next video in the series can be seen at: htt
From playlist THE "WHAT IS" PLAYLIST
Proof: Cartesian Product with Set Intersection | Set Theory
We prove that the cartesian product distributes over set intersection. That is, we'll prove that Ax(B intersect C) = (AxB) intersect (AxC). To prove this set theory result, we'll use what's sometimes called double inclusion. This means we'll prove Ax(B intersect C) is a subset of (AxB) in
From playlist Set Theory
Graph Theory: 49. Cartesian Product of Graphs
What is the Cartesian product of two graphs? We start with a reminder of what this means just for sets and then provide the formal definition for graphs. We include a few examples to become familiar with the idea and we also briefly discuss what a hypercube (or n-cube) is in graph theory
From playlist Graph Theory part-8
Proof: Cancellation Law for Cartesian Products | Set Theory
We prove the cancellation law for cartesian products. Suppose A, B, and C are sets with C nonempty. Then AxC=BxC. This is a straightforward set equality proof, we first have to consider the case where A is empty. Then, we'll suppose it is nonempty, and show A is a subset of B. It is the sa
From playlist Set Theory
What is a Tensor 6: Tensor Product Spaces
What is a Tensor 6: Tensor Product Spaces There is an error at 15:00 which is annotated but annotations can not be seen on mobile devices. It is a somewhat obvious error! Can you spot it? :)
From playlist What is a Tensor?
What is a Tensor 4: Cartesian Products
What is a Tensor 4: Cartesian Products
From playlist What is a Tensor?
CARTESIAN PRODUCTS and ORDERED PAIRS - DISCRETE MATHEMATICS
We introduce ordered pairs and cartesian products. We also look at the definition of n-tuples and the cardinatliy of cartesian products. LIKE AND SHARE THE VIDEO IF IT HELPED! Support me on Patreon: http://bit.ly/2EUdAl3 Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http
From playlist Discrete Math 1