(Abstract Algebra 1) Equivalence Classes

The definition of equivalence classes is given and several properties of equivalence classes are introduced.

[itjustmemyselfandi]

No matter how they know the topic, some teachers are really bad at teaching. They can't speak in the level of the students. Some of them speak like we're babies, and some of them speak like we're geniuses. However, some people can explain the things well. This person is one of them, thank you sir.

[ibraheemkhan]

The first example was the exact problem I had. This helped a lot, thanks!

[ferociouswaves]

Thank you so much for this video! I now understand equivalence relations and equivalence classes! May God bless you and shower you with joy and happiness!

[andreaLA]

Thank you so much for this video! It helped me a lot!!

[DanielMak]

is the disjunction in the very last proof an exclusive or inclusive disjunction? ([x]=[y] or [x]intersects[y]=null set)
if it's an exlusive disjunction (which seems more likely), then assuming one false and proving another seems a bit counterintuitive because that seems to apply only to inclusive disjunction

[ssbsnb]

In the iff proof could we start with x exists in [x]... therefore x~y? this would make the symmetry step unnecessary

[mohmd]

equivalence classes are sets????
am I right??

[alexturk]

this was so useful. 11 minutes saved me hours trying to decipher my textbook

[lightnightsky]

Bro you have no idea how these videos have saved me. Thank you so much! You make everything make so much sense!

[danielstone]

Nice! I am trying to learn Abstract Algebra on my own. I know it is ambitious, but wish me luck and keep making these vids!!!

[jongallagher]

Legend has it someday learnifyable will return.... !

[alisondunning]

Thank you! At 9:17, wouldn't it have been more straightforward to start with y being an element of [x], since [x] := {y | x ~ y}, and from [x] = [y] we can just imply that y is an element [y]?

[ianz.]

Thanks a lot. you are a life saver. found your videos at the right time. do you also have a problem set for this topic?

[adi-sngh]

After watching a lot of videos on this topic, I stumbled upon this video and this is the only video that was able to explain me this topic. (My textbook just confused me)

[mathsical]

Thank you so much! I've been searching for abstract algebra videos all over youtube and your videos are literally the only ones I understand!
For the last example, would you also have to look at the case where [x]=/=[y] and show they have to be disjoint?

[edwizecorner]

well explianed and i am curious about which software you are using to explain, can you plz name it

[parkermilligan]

You should consider private tutoring. I would pay you. I'm in my university's proofs class right now. Fun stuff! Btw, great videos.

[aryankumarprasad]

Thanks. I am into the second week into a Group theory class, and now I understood what its all about.

[ashmitasingh]

Thanq u so much the way u had explained by giving the example was really nice.

[Bemath_kh]

More videos please. I love your teaching ♥️♥️♥️🙏