Equivalence Relations Definition and Examples
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Equivalence Relations Definition and Examples. This video starts by defining a relation, reflexive relation, symmetric relation, transitive relation, and then an equivalence relation. Several examples are given.
From playlist Abstract Algebra
Equivalence Relation on a Group Two Proofs
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Equivalence Relation on a Group Two Proofs. Given a group G and a subgroup H of G, we prove that the relation x=y if xy^{-1} is in H is an equivalence relation on G. Then cosets are defined and we prove that s_1 = s_2 iff [s_1] = [s
From playlist Abstract Algebra
The picture in the lecture was taken from Wikipedia: https://en.wikipedia.org/wiki/Demographics_of_the_United_States#/media/File:USA2020dec1.png
From playlist Abstract Algebra 1
Put all three properties of binary relations together and you have an equivalence relation.
From playlist Abstract algebra
Cosets and equivalence class proof
Now that we have shown that the relation on G is an equivalence relation ( https://www.youtube.com/watch?v=F7OgJi6o9po ), we can go on to prove that the equivalence class containing an element is the same as the corresponding set on H (a subset of G).
From playlist Abstract algebra
This video is a full introduction to equivalence relations. Timestamps: 0:00 What is a relation? 3:02 Terminology - A Relation defined on a Set 4:02 Equivalence Relation Definition 7:18 Reflexive 9:18 Symmetric 11:48 Transitive Thanks for watching! Comment below with questions, and make
From playlist Proofs
Equivalence Classes Partition a Set Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Equivalence Classes Partition a Set Proof. This video starts with the definition of an equivalence class and then proves that for a given set S and an equivalence relation R on S, we can write S as the disjoint union of it's equival
From playlist Abstract Algebra
Prove that R is an Equivalence Relation on Z: xRy if x + 3y is even
In this video we define a relation R on the set of integers Z as follows: We say x R y if x + 3y is even. We prove that R is an equivalence relation on Z. To do this we show that R is reflexive, symmetric, and transitive. The pencils I used in this video: https://amzn.to/3bCpvpt The pape
From playlist Relations
Equivalences and Partitions, Axiomatic Set Theory 2 2
Defining equivalences and partitions of sets, and proving some theorems about their relations to each other. My Twitter: https://twitter.com/KristapsBalodi3 Equivalence Relations:(0:00) Partitions:(9:22) Connecting Equivalence and Partitions:(14:09) Representatives:(27:04)
From playlist Axiomatic Set Theory
equivalence relations -- proof writing examples 17
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From playlist Proof Writing
Intro to proofs April 20, 2021
Suggest a problem: https://forms.gle/ea7Pw7HcKePGB4my5 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn.net Randolph College Math: http://www.randolphcollege.edu/ma
From playlist Super Lo-fi in class videos
Algebraic Topology 1.3 : Path Homotopy and Product (Animation Included)
In this video, I introduce the concept of path homotopy, as well as the product of paths. This is in build-up to the fundamental group. I talk about the line homotopy, convex sets, and general theorems regarding products of paths and homotopy. Translate This Video : Notes : None yet Patre
From playlist Topology
Introduction to University Mathematics: Lecture 4 - Oxford Mathematics 1st Year Student Lecture
This course is taken in the first two weeks of the first year of the Oxford Mathematics degree. It introduces the concepts and ways of mathematical thinking that students need in the years ahead. Much of the context will be familiar from high school but the way we think and write about i
From playlist Oxford Mathematics Student Lectures - Introduction to University Mathematics
Fundamentals of Mathematics - Lecture 25: Quotient Maps (Real Projective Line, Modular Arithmetic)
course page - https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html videography - Eric Melton, UVM
From playlist Fundamentals of Mathematics
Abstract Algebra | Equivalence Relations
We give the definition of an equivalence relation and some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
What_is_a_Manifold_Lesson_16: The Mobius strip
What is a Manifold? Lesson 16: The Mobius strip The Mobius strip is a quotient space, a manifold, and a fiber bundle. In this lecture we define the Mobius strip as a quotient space and prove that it is a manifold.
From playlist What is a Manifold?
Here is fundamental mathematical result in mathematics, namely: any metric space, no matter how crazy it is, can be completed. After watching this video, it should be no surprise that the rational numbers can be completed to get the real numbers. The proof itself is very neat and kind of m
From playlist Topology
Lots of group isomorphism examples.
We present several examples of group homomorphisms and isomorphisms applying the first isomorphism theorem. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Commutative algebra 16 Localization
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we construct the localization R[S^-1] of a ring with respect to a multiplicative subset S, and give some examp
From playlist Commutative algebra
Important Math Proof: The Set of Equivalence Classes Partition a Set
In this video I prove a very important result in mathematics. Given an equivalence relation R on a nonempty set A, the set S of equivalence classes of A is a partition of A. Stated another way, this result says we can write A as a disjoint union of equivalence classes. The pencils I used
From playlist Relations