Equivalence Relations Definition and Examples

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Equivalence Relations Definition and Examples. This video starts by defining a relation, reflexive relation, symmetric relation, transitive relation, and then an equivalence relation. Several examples are given.

[@gob9940]

you didn't go through each example, you just said "it turns out" that each case was either reflexive, symmetric, or transitive. This video doesn't help because there are steps left out of how you determined each to be reflexive, symmetric, etc.

[@darkkupo5162]

there are no more steps. You have to be able to think ;)

[@roelin360]

@@darkkupo5162 why would you even be on a video to learn how to do these things if you could already do it?

[@wywlf6912]

@@darkkupo5162 dumbass

[@RonChase21]

Thank you for the video but I wish you would have explained why each problem was Reflexive, Symmetric, or transitive. That would have made everything clearer

[@stevefreed3646]

you showed an example but didn't bother explaining it

[@vocaljazz32]

How do you prove that the congruence modulo is an equivalence relation?

[@War_lord_K2]

congruence modulo means when two numbers are divided by the same number, the remainders are equal. And we know, "equal to" is an equivalence relation.

[@kcaldwell_]

For the last example, where can i find the proof that you referenced? In the other video? Can't seem to find it. Thanks

[@Theboss4103]

in the example with S=(complex numbers) surely it is transitive because if x is not = to y and y is not = to z then x is not = to z

[@1989DP3]

It's not transitive. If x!=y and y!=z that does not conclusively prove any relation between x and z.

[@jakemoran287]

No, because x and z could equal eachother but still not equal y. ie, x=1,y=2,z=1

[@1409musiclover]

great examples. thank you.

[@yamatanoorochi3149]

7:27 if x is related to y then y is related to x. Symmetric ✓ x is also related to itself because x has the same parents as itself. Reflexive ✓ if y is related to z because the have the same parents then x is also related to z. Transitive ✓ So Equivalent ✓

[@quintustheophilus9550]

I have a question, What does S1, S2, S3 have to be? Just any element of the Set S? Also, do all the elements of a set have to follow the equivalence relation?

[@Mage_Chartreux]

The nature of the conditions for a relation (set of ordered pairs) to be an equivalence relation means that all members of the set must satisfy the transitive, symmetric, and reflexive properties. (These are relation properties, so if some member of the set violates the definition of one of those properties, then you can't say the set has that property.)

[@kululu4413]

Thank you! Great examples.

[@yamatanoorochi3149]

I don't understand the last example, at all What prerequisites do I need

[@TheMathSorcerer]

[@pontuseriksson2825]

Great video :)

[@brentgallagher3603]

good examples

[@TheMathSorcerer]

thx!

[@xpertstrategist2216]

Let A = Z and let R = {(x, y): x, y ∈ A, x2 = y2}. Prove that R is an equivalence relation

[@VeNtICeO]

Thanks

[@1989DP3]

Great video, helped me a lot. Thanks!

[@TheMathSorcerer]

awesome glad it helped!!

[@ruthzkycanz]

If bRa and aRb does it imply that a=b?

[@marioburgos8656]

I think that it is transitive in the example with S=(complex numbers). Right?

[@camilomuianga7865]

Yes, definetely you are right! I was solving it now, and i've prooved it!

[@reyichen1382]

great examples

[@TheMathSorcerer]

Thank you!

[@Eis461]

12:05 where is the video link

[@kae5315]

Good video! Thanks!

[@TheMathSorcerer]

Kathleen Epperson glad it helped!!

[@abdussy.6547]

HEYY BOSS. I NEED YOUR HELP. THİS İS MY LAST CHANCE TO PROVE AN EQUALITY. CAN YOU WRITE YOUR E MAIL? THANK YOU BOSS I LOVE YOU. ( THE DEADLİNE İS TODAN 10 P.M.)