How to Prove a Relation is an Equivalence Relation

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

Thank you very much sir love from India ❤

thx for the video, keep up the good energy

He is awesome

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

I LOVE YOUU

what a great video

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

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?

u just saved my assignment, thankyou

Awesome video!!!!!

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

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 🤣

I LOVE YOU

Amazing video! Thank you so much.

XD

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

Some say he smoked a whole bag of meth before making this one.

This was very very helpful! Great method of teaching

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

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💪

Wild, you used to look like that?

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

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

this is way better than how my prof explained this topic

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

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

Replace my professor please

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?😅

nice to see exotic joe finally learned math

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

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

Thanks for this vid. It helped me a lot <3

math is a helluva drug

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.

When Joe Exotic is better at math than you

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

what a knowledge man

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

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

You are the best!

Well this was fun

Thank you so much

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

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

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.

Really Helpful Thank you very much

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

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