(Abstract Algebra 1) Definition of an Equivalence Relation

The definition of an equivalence relation is given along with three examples.

[@oluwafunmilayoolapade7600]

Infact this has increase my interest in algebra. I hope you give this type of teachings on p-groups. Thanks for your contribution.

[@RonaldModesitt]

Excellent videos! Do you use a book as the basis of your videos. If so I would appreciate knowing the title and author.

[@soumyashreeram1012]

you are a wonderful teacher. Thank-you for helping us kids out. :)

[@pinklady7184]

At beginning, I have learned that ~ means "be equivalent to." Thanks. I keep listening to video. Edit. I just subscribed.

[@nick6269]

Thanks a lot! Examples really help to make it more concrete

[@Lyes_Abdellatif]

The best 👍💯

[@ethanhsu5553]

Thank you.It is perfect

[@kajalbharti1118]

My university teach nothing in this covid period, so I was really relax for the online exams. But suddenly they notified us the exam be conducted in offline mode. I was freaked out.....I don't know nothing, thank you so much sir. I wish you were my teacher. Thanks!!

[@yayitsellen1]

Thank you so much, very helpful :)

[@rj126]

Thank you, I wish that you are my teacher

[@ys1940]

Your videos are awesome

[@lucjandespiegeleire454]

these videos realy help to understand my textbooks witch are so freaking difficult, thanks =)

[@KanoBoom]

pattern: On the set ?, let x ~ y if and only if (condition), for any x,y ∈ ?

[@ruthzkycanz]

Can I have a question? if bRa and aRb does it imply that a=b?

[@alancristopher3539]

How Prove ∼ is an equivalence relation: x∼y if and only if y=hxt. H,T subgroups of G?

[@juanjaimescontreras1798]

Great videos, I learned so much from your videos, Thank You

[@tilkesh]

I too !!!!!!

[@user-bq6dd7rn2d]

Hello sir. Can you please solve this one. R = Z×Z defined by nRm off nm≥0.

[@athira.k4291]

Thank u lot. It helped me. Thank u

[@meriroshi1800]

Thank you!!! :)

[@victorserras]

You need to remove the "any" in the definition of your relation for it to be an equivalence relation. Only then the rest of what you said holds.

[@aliahiqbal3474]

thank you.

[@upasnahbalkissoon438]

hi morning sir, can you plz suggest me an algebra pdf

[@eesueryu4489]

I found one example is not correct: m~n iff m-n is divisibke by 3. Right to left direction is okay, but the opposite doesn't hold because equality or equinumerosity is equivalence relation, so even though a relation is equivalent, that doesn't imply that the relation is being divisible by 3.

[@seriousmax]

"for any m,n in Z" is confusing, because the relation won't hold for every m,n in Z... Or am I wrong?

[@learnifyable]

I agree, it is a little confusing. It is appropriate to say "for any m, n in Z" here since you are allowed to "compare" any two values of m and n to see if they are equivalent. In fact, if you watch the video on the relationship between equivalence relations and partitions, then you will see that equivalence relations carve up the set into a bunch of non-overlapping subsets.

[@chrisjfox8715]

learnifyable so it only has to be true for at least one value, not all values? The word "any" implies that it must be all

[@k_h4258]

How did we get m - p = (m-n) + (n-p) ?

[@janplonka7143]

if m-n= 3a and n-p=3b then => m= 3a-n and p= n-3b then substituting we have m-p= (3a-n) - (n-3b) = 3a-n+n+3b= 3(a+b)

[@ronnies.3440]

Thanks, Jan!

[@musicdragon966]

Why is m-p =(m-n) +(n-p) I don't get that step

[@prosperanku6130]

When you Expand the right hand side the two n will cancel out