How to Prove a Relation is an Equivalence Relation

How to Prove a Relation is an Equivalence Relation
Proving a Relation is Reflexive, Symmetric, and Transitive;i.e., an equivalence relation.
I had never done this problem before so there are moments where you can see me pause briefly because I had to figure it out.

[@Joel-js2gk]

This guy teaches me in 5 minutes things that I've struggled to understand after hours of studying teacher's notes. My teacher is actually really good for the most part but I think the majority of teachers struggle with over complicating matters. Or maybe I just don't pay enough attention in class 🤣

[@Sigmafemale..14]

Obviously both came to the conclusion bruh

[@erjon6569]

This guy is the most American looking person I've ever seen Thanks by the way 🙂

[@TheMathSorcerer]

Lol

[@isabelamaro7722]

Oh my gosh! You thought better than my professor! I love that you repeat everything multiple times and show where you got it from!

[@raminhussain2740]

Goes straight to the point, well explaned I love it. Keep up the amazing work!

[@isamkarroum8716]

finally someone who knows what they're talking about and also has an accent i can decipher

[@laylanguyen1553]

This was very very helpful! Great method of teaching

[@abrarrahman6302]

Really great explanation. Thank you. Great teachers like you make studying worthwhile.

[@TheMathSorcerer]

aww thanks man!

[@nandinichaurasiya8362]

Nice way of explanation, thanks a lot😊😊

[@liem8687]

u just saved my assignment, thankyou

[@bingusdingus8239]

Thank you so much, as someone with adhd you were able to actually keep my attention!!

[@TheMathSorcerer]

success!

[@realyours643]

the explanation was really good, i watch it while i was laying down, but it got to my brain. really great explanation, thank you sir, keep doing your hard work💪

[@TheMathSorcerer]

Awesome

[@jessesambro9535]

did you do a line of coke before this video. Good video tho

[@wowowowzzz]

2 lines

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Thats the best thing about this guy XD

[@TheMathSorcerer]

Lol

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thx for the video, keep up the good energy

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Thank you very much sir love from India ❤

[@gerechte1]

Can you please start teaching at my university? The current prof even looks just like you but with 10 hours less sleep

[@TheMathSorcerer]

Lol

[@haleyanderson2258]

lol

[@gpiludu]

Thanks, Sorcerer Cowboy. This was a good explanation.

[@TheMathSorcerer]

thank you!!

[@wytewolf77]

Tiger King is a smart cookie, good vid, cheers.

[@JamesBrodski]

Amazing video! Thank you so much.

[@saburirasheed4070]

Nice video. I also discover that we can prove the transitive property by adding a + d = b + c and c + f = d + e.

[@TheMathSorcerer]

yup:)

[@Faylasuf57]

Currently learning this stuff in my theoretical foundations class haha. Good stuff man, you always put out great content. How did you feel about these when you were first introduced to them?😅

[@TheMathSorcerer]

I didn't understand what a relation was at first, struggled hard lol

[@Sigmafemale..14]

@@TheMathSorcerer Not bad cos every master was once a beginner

[@natholdelessa6369]

Really Helpful Thank you very much

[@Lionfish5656]

What if instead of (a,b) ~ (c,d), you have a + b? I'm trying to follow the video format, but it's very confusing. Perhaps I'm taking way too much meletonin.

[@ralphcastro8661]

this is way better than how my prof explained this topic

[@bunstie5208]

hi, i pretty much have the exact same question but instead of outers + inners its, a+b = c+d. because addition is commutative i believe i can just rearrange to suit my question?

[@saipansmall]

Why do you add the inner and outer elements together? (A,B)~(C,D) becomes A+D=B+C

[@bestdeals-amazonus7779]

Amazing! Thank you!

[@TheMathSorcerer]

np:)

[@jeboitonny1901]

Thanks for this vid. It helped me a lot

[@TheMathSorcerer]

Glad it helped!

[@xIEBx1]

You are the best!

[@TheMathSorcerer]

❤️

[@princekumarsingh243]

what a knowledge man

[@TheMathSorcerer]

Thx

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what a great video

[@Thegamer-kf8zz]

Awesome video!!!!!

[@TheMathSorcerer]

Thanks!!

[@epicblubber]

This helped a lot thanks man. Nice hat by the way!

[@TheMathSorcerer]

Excellent !!

[@lemone9639]

It's 3am, I was about to do three shots of expresso cause I wasn't able to understand this all night and I need to prove a point to my prof at 9. You just gave me an hour of sleep. Thanks

[@philmccavity]

Makes me feel better watching math pros get confused doing proofs.

[@XxYoShIkOgAkIxX]

Coke is your friend lol. Nice video, I see you have fun doing what you are doing :)

[@user-gx9lr2mh2i]

nice to see exotic joe finally learned math

[@shawnl7966]

Your videos are really great. If I may give my feedback, I preferred the ones that were just a blackboard. I think adding in mental processing of watching a person and all that comes with that is distracting. Goal is just to focus on the math for me.

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He is awesome

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this video + these comments made my day lmao, loved it. ahh thank you!

[@TheMathSorcerer]

I'm so glad!

[@Caarve]

Thank you so much

[@TheMathSorcerer]

You're most welcome:)

[@user-ee4yx2hs3k]

Thank you bro

[@TheMathSorcerer]

Np

[@creepdrgaming1205]

Convert the condition to a-b=c-d, then every equivalent point appears on a line.

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I LOVE YOU

[@itslogic9583]

Well this was fun

[@TheMathSorcerer]

👍

[@Hi_Brien]

Wild, you used to look like that?

[@TheMathSorcerer]

LOL wow yeah that facial hair, humm, I wonder if I should grow it back haha

[@Hi_Brien]

@@TheMathSorcerer so right now I am working with an equivalence relation. Specifically I have to show that bijectiveness defines an equivalence relation on sets. I can think of a few bijective relations that are not equivalence relations though, simply because of reflexivity, f(a) = a means the only function that works is an identity function like i: A->A, is there some kind of misinterpretation I am doing?

[@Hi_Brien]

@@TheMathSorcerer My current thought which I have very little faith towards is just showing that ~ is bijective? Is that what the prompt "prove that bijectiveness defines an equivalence relation"

[@Hi_Brien]

Update: The actual prompt was isomorphism defines an equivalence relation. I just renamed isomorphism wrongly in my head.

[@Uax101]

math is a helluva drug

[@sivatharshan]

i understood this and i dont know what it is and what we doing.only i want is pass the exam tomorrow.

[@TheMathSorcerer]

👍

[@sivatharshan]

@@TheMathSorcerer how can we do that for if a-b

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I LOVE YOUU

[@Caarve]

6:08 LMFAO that facial expression

[@TheMathSorcerer]

LOL

[@ryanraymond8299]

Confuse a function and an equation in front of your professor, and this is the last thing you see.

[@coreylahey1397]

When Joe Exotic is better at math than you

[@AMo1-]

Replace my professor please

[@TheAAZSD]

Good video. The hat is not sorcerous enough, however.

[@TheMathSorcerer]

hahahahaha thanks:)

[@TheAAZSD]

@@TheMathSorcerer That said, this is all really enjoyable content and super helpful for seeing different takes on what I'm currently learning.

[@TheMathSorcerer]

@@TheAAZSD awesome:)

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XD

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Can you be my dad? I could send you math research papers when I write them :)

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Dude.. this is not a bidding contest, take off the hat and slow down 😂

[@TheMathSorcerer]

LOL!!!!!!!!!!!!!!!!!