Prove that R is an Equivalence Relation on Z: xRy if x + 3y is even

Подписаться 941 тыс.

Просмотров 14 тыс.

50% 1

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: amzn.to/3bCpvpt
The paper I used in this video: amzn.to/3OQ8nuM
(the above links are my affiliate links)
If you enjoyed this video please consider liking, sharing, and subscribing.
Udemy Courses Via My Website: mathsorcerer.com
Free Homework Help : mathsorcererforums.com/
My FaceBook Page: / themathsorcerer
There are several ways that you can help support my channel:)
Consider becoming a member of the channel: / @themathsorcerer
My GoFundMe Page: www.gofundme.com/f/support-ma...
My Patreon Page: / themathsorcerer
Donate via PayPal: paypal.com/donate/?cmd=_s-xcl...
***********Udemy Courses(Please Use These Links If You Sign Up!)************
Abstract Algebra Course
www.udemy.com/course/abstract...
Advanced Calculus Course
www.udemy.com/course/advanced...
Calculus 1 Course
www.udemy.com/course/calculus...
Calculus 2 Course
www.udemy.com/course/calculus...
Calculus 3 Course
www.udemy.com/course/calculus...
Calculus 1 Lectures with Assignments and a Final Exam
www.udemy.com/course/calculus...
Calculus Integration Insanity
www.udemy.com/course/calculus...
Differential Equations Course
www.udemy.com/course/differen...
Differential Equations Lectures Course (Includes Assignments + Final Exam)
www.udemy.com/course/differen...
College Algebra Course
www.udemy.com/course/college-...
How to Write Proofs with Sets Course
www.udemy.com/course/how-to-w...
How to Write Proofs with Functions Course
www.udemy.com/course/how-to-w...
Trigonometry 1 Course
www.udemy.com/course/trigonom...
Trigonometry 2 Course
www.udemy.com/course/trigonom...
Statistics with StatCrunch Course
www.udemy.com/course/statisti...
Math Graduate Programs, Applying, Advice, Motivation
www.udemy.com/course/math-gra...
Daily Devotionals for Motivation with The Math Sorcerer
www.udemy.com/course/daily-ma...
Thank you:)

Опубликовано:

11 июл 2022

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 12

@llbillnyell Год назад

This is the most detailed and understandable video I've seen through all of these equivalence relation videos. Thank you!

@TheMathSorcerer Год назад

You are very welcome!

@thetheoreticalnerd7662 2 года назад

I think a nice way to approach the symmetric property is by rewriting a + 3b as (a + b) + 2b. Indeed, the second term in the sum is even and hence does not change the parity of the expression, and therefore a + b is even (by assumption a R b => a + 3b is even). Now if we rewrite b + 3a as (b + a) + 2a, by a similar argument this value is even iff b + a is even. But we have already shown that a + b is even, so by commutativity of addition this completes the proof of the symmetric property.

@rageprod 2 года назад

Very cool. What particular math subject is this?

@patricia.antlitz Год назад

Discrete mathematics

@Albertobelmonte9 2 года назад

Nice 😁

@5Stars49 2 года назад

Nice 👍😊

@erickmacias5153 2 года назад

It might seem dumb, but what exactly is a Relation? I find it to abstract, i understand the proof and everything, but I have a problem trying to imagine what are we actually proving.

@AjayKumar-hh6hx 2 года назад

It is not a dumb question at all. I have difficulty understanding mathematics when i don't understand its application. Relations and functions can be used in all fields. A relation is basically the link between two or more quantities. For example, temperature and volume of a room, or your relationship with a distant family member. You can use reasonings based on this subject to figure out the relation between or among any entities. What are the places you can travel to with 1 gallon of petrol in the tank? That's also a question you can answer through this subject.

@AjayKumar-hh6hx 2 года назад

Relations become very important when you are a statistician in any field. It is also the foundation of computer programming.