(Abstract Algebra 1) Equivalence Classes

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

[@alexturk6389]

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!

[@yondabigman4668]

fr, I thought this stuff was impossible

[@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!

[@learnifyable]

Thank you for the kind words!

[@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.

[@jongallagher4719]

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

[@danielstone5810]

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!!!

[@ibraheemkhan9773]

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

[@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?

[@pramila1803]

Thank you!! These are very clear step by step videos ❤️🙏

[@aryankumarprasad1574]

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

[@geogaddi84]

Great explanations. Thanks

[@andreaLA222]

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

[@utility00]

Great video

[@Rohitgupta0908]

Awesome explanation

[@ajay42822]

Thanks...that helped a lot... keep posting....

[@shawnkoo3099]

Excellent!

[@ashmitasingh7029]

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

[@gulligagardinen]

Perfect! Thank you! :)

[@leilajabari5961]

very useful thanks.

[@Bemath_kh]

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

[@arnabchowhan3488]

shabbash gooooood yaar

[@Francesabc]

this helped a lot. thank you!

[@learnifyable]

No problem! I'm glad I could help.

[@kwame7003]

I really appreciate it

[@AkhileshKaur]

Thank you a lot for making this.

[@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)

[@navjotsingh2251]

There’s two ways of doing math, the intuitive way ( like this video) or the textbook way, I hate textbooks and don’t really use them in my studies because the ones we get are so boring and unintuitive.

[@unknown-pe1oq]

Thaks for efforts

[@ianz.0]

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?

[@pranesh061]

Nice video. What device did you use to make this great explanation?

[@Ghost_of_Morisset]

Thanks for this

[@alisondunning2446]

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]?

[@subhashmehta7809]

well done

[@parkermilligan7503]

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

[@athira.k4291]

Thank you

[@sfhan]

great video, thanks!

[@learnifyable]

Shufang Han I'm glad I could help.

[@tmendoza6]

holy hell this was great!

[@DanielMak1234]

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

[@aydiology]

Man Bear Pig The phrase "either … or" generally implies an exclusive disjunction.

[@edwizecorner7652]

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

[@theunknown4209]

great hand writing. looks like you trained as an architect

[@amsainju]

Thank you very much

[@learnifyable]

+Arpan Man Sainju You're welcome.

[@ssbsnb1200]

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

[@learnifyable]

+ssbsnb1 Yes, that would work too. A short proof made even shorter!

[@danibhutta9803]

Thanks Brother...

[@learnifyable]

+Dani Bhutta I'm glad I could help.

[@mohmd252]

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

[@excorpse]

yes

[@HaniYahya9]

Why -1 is not divisible by3 but -6 is? Thanks

[@latishacooper11]

Because -1 divided by 3 would give you -1/3 but -3 divided by 3 would give you -3/3 = -1 same for -6/3 = -2. For a number to be divisible by another number it should not leave and remainders or result as a fraction.

[@x87-64]

-1 = 3*-1 + 2 Hence when -1 is divided by 3, it leaves a remainder of 2. But, -6 = 3*-2 + 0 Which means -6 / 3 doesn't leave a remainder or we can say -6 is divisible by 3.

[@Random-om8rq]

Noice

[@shikharmishra8818]

works better on 1.25x

[@adi-sngh]

10 people failed their math test.

[@BennettBush]

bad

[@user-zn7sk2rc8g]

Thank you

[@learnifyable]

You're welcome